Integrate x^2/(1+x^2)dx
Unlike if we had just x in the numerature, here the chain rule will do us no good. Integration by parts in this case also is little help - we end up with expressions at least as difficult as we started with. For example:
Int x2/(1+x2)dx = x2tan-1x - Int 2x tan-1x dx
In this case, a very simple approach is to simply add and subtract 1 from the denominator:
Int x2/(1+x2)dx = Int (x2+1-1)/(1+x2)dx= Int (1+x2)/(1+x2) - 1/(1+x2)dx = Int 1 - 1/(1+x2)dx
From here, do you know know you to solve the problem?
LH
Related Maths IB answers
All answers ▸Given that y = -16x2 + 160x - 256, find the value of x giving the maximum value of y, and hence give this maximum value of y.
How do you calculate the probability P(X < x) for a normally distributed random variable X?
Given the function y=f(x), where f(x)=(e^x-e^(-x))/2, find its inverse f'(x).
The sum of the first n terms of an arithmetic sequence is Sn=3n^2 - 2n. How can you find the formula for the nth term un in terms of n?