# Morning distinguished Engineers

#### Breeze

Joined Jun 30, 2015
24
I need help with simplifying this integral,i have tried a couple of formulae but with no success

2x+1/3x^2+3x+5 dx...see the uploaded attachment of my attempts at solving it

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#### RBR1317

Joined Nov 13, 2010
668
Attached are the output of two different symbolic math engines. The software does not explain how it does the evaluation.

#### Papabravo

Joined Feb 24, 2006
17,011
The integral is in the proper form of

$$\frac{du}{u}$$

I don't see the problem.

#### Russmax

Joined Sep 3, 2015
82
More accurately, Papa, you do see the problem and the solution.

#### Papabravo

Joined Feb 24, 2006
17,011
Yes I do. Once the constant factor, k, is removed the numerator is the derivative of the denominator, and the answer follows as:

$$k\cdot ln(u)$$​

#### WBahn

Joined Mar 31, 2012
26,398
I need help with simplifying this integral,i have tried a couple of formulae but with no success

2x+1/3x^2+3x+5 dx...see the uploaded attachment of my attempts at solving it
One thing you need to do is to stop being sloppy with your notation. What you have written above is

$$\int \; \( 2x \; + \; \frac{1}{3}x^2 \; + \; 3x \; + \; 5$$ \; dx
\)

Sloppiness in notation leads to (or results from) sloppiness in thought.

#### Breeze

Joined Jun 30, 2015
24
Thank you all for your help have actually found the answer following your leads,i have seen where my mistake was,i had somehow overlooked the concept in my notes,so i actually found it some moments ago of course with the hints from all of you.I want to apologize for my sloppiness as it were,as a newbie in Engineering i certainly have a lot of concepts to learn and master,needless to say i need to quickly master the art of writing in proper notation,i will as a matter of urgency get myself well acquainted wit TEX.I want to express my heartfelt gratitude at your tireless efforts in helping me through my schooling as an aspiring budding engineer.

#### Breeze

Joined Jun 30, 2015
24
One thing you need to do is to stop being sloppy with your notation. What you have written above is

$$\int \; \( 2x \; + \; \frac{1}{3}x^2 \; + \; 3x \; + \; 5$$ \; dx
\)

Sloppiness in notation leads to (or results from) sloppiness in thought.
i am very sorry about my sloppiness,the above expression should actually be,find the integral of: (2x+1)/(3x^2+3x+5) dx

#### shteii01

Joined Feb 19, 2010
4,644
hm...
$$\frac{2x+1}{3x^2+3x+5}=\frac{2x}{3x^2+3x+5}+\frac{1}{3x^2+3x+5}$$
then
$$\int\frac{2x+1}{3x^2+3x+5}dx=\int\frac{2x}{3x^2+3x+5}+\frac{1}{3x^2+3x+5}dx=\int\frac{2x}{3x^2+3x+5}dx+\int\frac{1}{3x^2+3x+5}dx=2\int\frac{x}{3x^2+3x+5}dx+\int\frac{1}{3x^2+3x+5}dx$$
^ would finding two simpler integrals and then combining the results help?

#### Papabravo

Joined Feb 24, 2006
17,011
Conceivably it could also have been:

$$( \; 2x \; +\; \frac{1}{3x^2} \; +\; 3x \; + \; 5 \; )$$

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#### Papabravo

Joined Feb 24, 2006
17,011
...
would finding two simpler integrals and then combining the results help?
No it makes it harder. The key insight is that except for a constant the numerator is the derivative of the denominator.

#### WBahn

Joined Mar 31, 2012
26,398
Conceivably it could also have been:

$$(\;2x + \frac{1}{3x^2} +3x + 5)$$
Nope. Division and multiplication have equal precedence and are left associative. Thus the division is performed before the multiplication.

Highest priority -- exponentiation:

2x+1/3x^2+3x+5 = 2x+1/3(x^2)+3x+5

Next, multiplication and division, left to right:

(2x)+((1/3)(x^2))+(3x)+5

Next, addition and subtraction, left to right:

((((2x)+((1/3)(x^2)))+(3x))+5)

#### shteii01

Joined Feb 19, 2010
4,644
No it makes it harder. The key insight is that except for a constant the numerator is the derivative of the denominator.
You are right, it would not have helped. My freshman calculus textbook does not have that form in the table of integrals.

#### Papabravo

Joined Feb 24, 2006
17,011
One thing you need to do is to stop being sloppy with your notation. What you have written above is

$$\int \; \( 2x \; + \; \frac{1}{3}x^2 \; + \; 3x \; + \; 5$$ \; dx
\)

Sloppiness in notation leads to (or results from) sloppiness in thought.
Nope. Division and multiplication have equal precedence and are left associative. Thus the division is performed before the multiplication.
There are exceptions to the left associative rule: APL for one. But I agree, that it is the most common practice in many programming languages. Maybe we should all learn RPN and dispense with the ambiguity of infix notation.

$$2\; x\; *\; 1\; +\; 3\; x\; x\; *\; *\; 3\; x\; *\; +\; 5\; +\; /\;$$

or perhaps

$$2\; x\; *\; 1\; +\; 3\; x\; 2\; \^\; *\; 3\; x\; *\; +\; 5\; +\; /\;$$

On second thought -- maybe not.

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#### WBahn

Joined Mar 31, 2012
26,398
There are exceptions to the left associative rule: APL for one. But I agree, that it is the most common practice in many programming languages. Maybe we should all learn RPN and dispense with the ambiguity of infix notation.

$$2\; x\; *\; 1\; +\; 3\; x\; x\; *\; *\; 3\; x\; *\; +\; 5\; +\; /\;$$

On second thought -- maybe not.
Has nothing to do with programming languages (the TS's problem has nothing to do with programs). This is the (as far as I know) universal precedence rules taught in grade school.

I'm definitely a proponent of RPN, but postfix notation has the real potential to cause confusion when written out because the operands often run together -- that's probably why humans adopted infix notation a few centuries ago.

#### Papabravo

Joined Feb 24, 2006
17,011
You are right, it would not have helped. My freshman calculus textbook does not have that form in the table of integrals.
I find it hard to believe that:

$$\int \; \frac{1}{x} \; dx \; =\; ln(x) \; + \; C$$

is not there. All of mine do!

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#### Breeze

Joined Jun 30, 2015
24
I find it hard to believe that:

$$\int \; \frac{1}{x} \; dx \; = ln(x) \; + \; C$$

is not there. All of mine do!
i actually have found this particular formula in my text bk,thanks a lot

• Papabravo

#### Papabravo

Joined Feb 24, 2006
17,011
Has nothing to do with programming languages (the TS's problem has nothing to do with programs). This is the (as far as I know) universal precedence rules taught in grade school.

I'm definitely a proponent of RPN, but postfix notation has the real potential to cause confusion when written out because the operands often run together -- that's probably why humans adopted infix notation a few centuries ago.
It was supposed to be joke son. Kinda like the fantasy that we could adopt the metric system. You didn't think I was serious I hope.

#### joeyd999

Joined Jun 6, 2011
4,477
There are exceptions to the left associative rule: APL for one. But I agree, that it is the most common practice in many programming languages. Maybe we should all learn RPN and dispense with the ambiguity of infix notation.
In fact, RPN is far more computationally efficient than infix -- especially for low complexity hardware. It is for this reason that I have my own set of stack-based floating point libraries for my PIC work.

#### WBahn

Joined Mar 31, 2012
26,398
In fact, RPN is far more computationally efficient than infix -- especially for low complexity hardware. It is for this reason that I have my own set of stack-based floating point libraries for my PIC work.
Definitely no argument there.