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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int \frac{e ^{u^{\frac{3}{2}}} u}{2 t} 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

\frac{\partial}{\partial y} (ln (2 + x^{2} y^{2}))

t \cdot \frac{d y}{d t} + 14 y = \frac{1}{t}

\frac{d}{d x} (a^{x^{2}})

\int \frac{( ln ( x ) ) ^{2}}{x} d x

(3 x^{2} - 1)^{4}

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