How do you find the indefinite integral of $int (x^2+1)^3dx$ ?

Question

3399 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-24T16:30:09

Expand the integrand and integrate term-by-term.

$(x^2+1)^3 = x^6+3x^4+3x^2+1$

So

$int (x^2+1)^3 dx = int (x^6+3x^4+3x^2+1) dx$

$= 1/7x^7+3/5x^5+x^3+x +C$

How do you find the indefinite integral of int (x^2+1)^3dxint (x^2+1)^3dx?