integaration (1 Viewer)

[hantu_ah]

How to integrate x/(1+x^2) dx ??



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[biopia]

Sorry to say it, but this is quite an easy question. Looking at it, you can see that the numerator is half the derivative of denominator, meaning the answer will be (1/2)ln(1+x²) + C.

If you're having trouble seeing that relationship, you can approach the question with substitution. It takes a tad longer, but you still get the same answer.

let u = x²
du/dx = 2x
du/2 = x.dx

∫x.dx/(1+x²) then becomes
(1/2)∫du/(1+u)

As you can see, this is a simple logarithmic integration as above.

(1/2)∫du/(1+u) = (1/2)ln(1+u) [But u=x²]
Therefore ∫x.dx/(1+x²) = (1/2)ln(1+x²) + C

Hope that helps you further understand these kinds of questions! Sometimes, the simplest methods will help with the most complex problems, especially if you just can't see the way to approach the question. You'll learn to see what method to use as you practice more though. =]

Good luck.

 

[untouchablecuz]

How to integrate x/(1+x^2) dx ??



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[hantu_ah]

i know that is simple question, but im confuse to solve this integaral..but i will try..thanks

 

[hantu_ah]

if i have double integral
Example

 

[ronnknee]

Double integrals are not part of Mathematics Extension 2 syllabus

For interest, integrate the inside so that you get the answer above, then integrate it again with the new boundaries (0 and pi/4)