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 ▸IB exam question: Let p(x)=2x^5+x^4–26x^3–13x^2+72x+36, x∈R. For the polynomial equation p (x) = 0 , state (i) the sum of the roots; (ii) the product of the roots.
Integrate cos(2x)sin(2x)
Three girls and four boys are seated randomly on a straight bench. What is the probability that the boys sit together and the girls sit together.
How do I find the derivative of 2^x?