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
∫ 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 ? )
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!
To solve the integral of x(5+x^2)^10 using substitution, let's start by identifying the choices we made for substitution:
u = (5 + x^2), and
du = x dx.
Now, let's rewrite the integral in terms of u:
Integral of x(5+x^2)^10 dx = Integral of u^10 du = (1/11)u^11 + C.
But we aren't done yet. We still need to express the answer in terms of x, not u. To do this, substitute back the value of u:
(1/11)(5+x^2)^11 + C.
This expression should give you the correct answer.