∫(x3+1)5x2dx
Here, we apply substitution method I.e.
Let u=x3+1
⟹dxdu=3x2
⟹dx=3x21du
Replacing back, we have;
∫(u)5x23x21du =31∫u5du
Now we solve;
∫u5du
Here, we apply power rule;
Where we let;
∫undu=n+1un+1 With n=5 , we have;
=6u6
Replacing this back to 31∫u5du we have;
18u6
Now we undo the substitution
u=x3+1
18(x3+1)6 and we add a C to this, hence the final answer i.e.
18(x3+1)6+C
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