How do you find the integral ∫x2(x2+2)32dx ?
1 Answer
Aug 29, 2014
=12⋅x√2+x2+c , wherec is a constantExplanation :
=∫x2(x2+2)32dx
=∫x2x3(1+2x2)32dx
=∫1x(1+2x2)32dx Using Integration by Substitution,
let's assume
2x2=t then
−4xdx=dt
=∫−dt4(1+t)32
=−14∫(1+t)−32dt
=−14⋅(1+t)−12−12
=12⋅1√1+t+c , wherec is a constantSubstituting
t back,
=12⋅1√1+2x2+c , wherec is a constant
=12⋅x√2+x2+c , wherec is a constant
