How do you integrate x3√x2+1dx?

1 Answer
James
Apr 25, 2018

The answer (x2+1)525−(x2+1)323+c

Explanation:

Show the steps below

∫x3⋅(x2+1)12⋅dx

suppose:
u=x2+1
x=(u−1)12
du=2x⋅dx
dx=12x⋅du
the int become after suppose:

∫[√u−1]3⋅√u⋅12⋅√u−1⋅du

12∫[√u−1]2⋅√u⋅du

12∫(u−1)⋅√u⋅du=12∫u⋅√u−√u⋅du=12∫u32−u12⋅du

12[25⋅u52−23⋅u32]+c

u525−u323+c

(x2+1)525−(x2+1)323+c

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