Evaluate the following integrals. int x^210^{x^3}dx

Chaya Galloway 2021-02-24 Answered
Evaluate the following integrals.
x210x3dx
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Expert Answer

Asma Vang
Answered 2021-02-25 Author has 93 answers

The given integral is,
x210x3dx
Using substitution method of integration, on substituting x3 with t
x3=t
3x2dx=dt
x2dx=dt3
Then the transformed integral we get is,
I=10t3dt
=1310tdt
Using exponential rule, axdx=axln(a)+C
I=1310tdt
=13[10tln(10)]+C
On puttinf back the value of t, we get
I=10x33ln(10)+C
Therefore, the value of the given integral is 10x33ln(10)+C

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