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

Carol Gates

Carol Gates

Answered question

2021-02-12

Evaluate the integral using the indicated substitution.
2x(x2+1)23dx, u=x2+1

Answer & Explanation

Sally Cresswell

Sally Cresswell

Skilled2021-02-13Added 91 answers

Step 1
Consider the integrals,
2x(x2+1)23dx...(1)
Let, u=x2+1
du=2xdx
Step 2
Substitute all value in equation (1) then,
2x(x2+1)23dx=u23du
=u2424+C
Substitute back, u=x2+1
2x(x2+1)23dx=124(x2+1)24+C
Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-05Added 2605 answers

Answer is given below (on video)

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