Evaluate the integral by making the given substitution. \int x^{2}\sqrt

vestirme4

vestirme4

Answered question

2021-10-17

Evaluate the integral by making the given substitution.
x2x3+1dx, u=x3+1

Answer & Explanation

Nathanael Webber

Nathanael Webber

Skilled2021-10-18Added 117 answers

x2x3+1dx
Let u=x3+1du=3x2dx13du=x3dx
Apply the substitution
x2x3+1dx=x3+1ux2dx13du=u(13)du
13u12du
Integrate, apply undu=un+1n+1+C, so
13u12du=13(u3232)+C
2u329+C
Back - substitute u=x3+1
2(x3+1)329+C
Results:
2(x3+1)329+C

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