Hey I have a question for those that know Integration by parts.
The general formula is "Integral of fg' = fg - Integral of f'g"
My question is work out the Integral of tan^-1 (3x).
Now, take f = tan^-1 (3x) and g = 1; so g' = x and f' = What????

Question

Hey I have a question for those that know Integration by parts.
The general formula is "Integral of fg' = fg - Integral of f'g"
My question is work out the Integral of tan^-1 (3x).
Now, take f = tan^-1 (3x) and g = 1; so g' = x and f' = What???? <--- It will be in the form of 1/(a^2 + x^2) But the 3x is throwing me off and I need help; solutions please?

zepdrix · Answer

Hmm yah it looks like you have the right idea for this By-parts :D
Just getting stuck on the derivative of the arctan? Hmm let's see.

$$\huge \frac{d}{dx}\arctan(3x)=\frac{1}{1+(3x)^2}(3x)'$$

tainted · Answer

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