# Evaluate the integral using the indicated substitution. \int2x(x^{2}+1)^{23}dx,\ u=x^{2}+1

Evaluate the integral using the indicated substitution.
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Sally Cresswell
Step 1
Consider the integrals,
$\int 2x{\left({x}^{2}+1\right)}^{23}dx$...(1)
Let, $u={x}^{2}+1$
du=2xdx
Step 2
Substitute all value in equation (1) then,
$\int 2x{\left({x}^{2}+1\right)}^{23}dx=\int {u}^{23}du$
$=\frac{{u}^{24}}{24}+C$
Substitute back, $u={x}^{2}+1$
$\int 2x{\left({x}^{2}+1\right)}^{23}dx=\frac{1}{24}{\left({x}^{2}+1\right)}^{24}+C$
Jeffrey Jordon