How do you use substitution to integrate $(2x(x^2 + 1)^23)dx$ ?

Question

6531 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-16T21:23:50

$int[2x(x^2+1)^23]dx=1/24(x^2+1)^24+C$

Use the substitution : Let $u=x^2+1$

Then $du=2xdx$ so this can be plugged into the integral. It may help to rewrite it so $2x$ and $dx$ are next to one another:

$int(x^2+1)^23(2xdx)$

We may hence write the original integral in terms of x into a new equivalent integral in terms of u as follows :

$intu^23du=u^24/24+C$

We now substitute back in terms of x to obtain the final answer as $(x^2+1)^24/24+C$

How do you use substitution to integrate (2x(x^2 + 1)^23)dx(2x(x^2 + 1)^23)dx?