Question

Calculate the following integrals using substitution
a) Integral of x(5+x^2)^10 dx , where u = (5 + x^2)

So, x(5+x^2)^10 dx
u = (5 +x^2)
du= x

The answer should be;
Integral of (u)^10 = [u/11]^11 + C = [(5+x^2)/11]^11 + C
But it say wrong answer

Answer 1

∫ x(5+x^2)^10 dx

= (1/22)(5 + x^2)^11 + c

check by taking the derivative, it works.

(did you forget to consider that the derivative of 5+x^2 = 2x ? )

Answer 2

Yes, my mistake I though du was = x dx, but it was equal to 2x dx, so I needed to multiply it by 1/2, thx!