What is the integral of e^{t^3}t^2 ?

The integral of e^{t^3}t^2 is 1/3 e^{t^3}+C

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integral of e^{t^3}t^2

\int e^{t^{3}} t^{2} d t

\frac{1}{3} e^{t^{3}} + C

Solution steps

\int e^{t^{3}} t^{2} d t

Apply u-substitution

: \int \frac{e ^{u}}{3} d u

= \int \frac{e ^{u}}{3} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= \frac{1}{3} e^{u}

Substitute back

u = t^{3}

= \frac{1}{3} e^{t^{3}}

Add a constant to the solution

= \frac{1}{3} e^{t^{3}} + C

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What is the integral of e^{t^3}t^2 ?
The integral of e^{t^3}t^2 is 1/3 e^{t^3}+C