What is the integral of 5t^2e^{(t^3)/3} ?

The integral of 5t^2e^{(t^3)/3} is 5e^{(t^3)/3}+C

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integral of 5t^2e^{(t^3)/3}

\int 5 t^{2} e^{\frac{t ^{3}}{3}} d t

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

Solution steps

\int 5 t^{2} e^{\frac{t ^{3}}{3}} d t

Take the constant out:

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

= 5 \cdot \int t^{2} e^{\frac{t ^{3}}{3}} d t

Apply u-substitution

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

= 5 \cdot \int \frac{e ^{\frac{u}{3}}}{3} d u

Take the constant out:

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

= 5 \cdot \frac{1}{3} \cdot \int e^{\frac{u}{3}} d u

Apply u-substitution

: \int e^{v} \cdot 3 d v

= 5 \cdot \frac{1}{3} \cdot \int e^{v} \cdot 3 d v

Take the constant out:

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

= 5 \cdot \frac{1}{3} \cdot 3 \cdot \int e^{v} d v

Use the common integral:

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

= 5 \cdot \frac{1}{3} \cdot 3 e^{v}

Substitute back

= 5 \cdot \frac{1}{3} \cdot 3 e^{\frac{t ^{3}}{3}}

Simplify

5 \cdot \frac{1}{3} \cdot 3 e^{\frac{t ^{3}}{3}} : 5 e^{\frac{t ^{3}}{3}}

= 5 e^{\frac{t ^{3}}{3}}

Add a constant to the solution

= 5 e^{\frac{t ^{3}}{3}} + C

\int \frac{5 x ^{2}}{e ^{x}} d x

\frac{\partial}{\partial x} (e^{- 2 t} cos (2 x))

\frac{\partial}{\partial x} (sec (x) tan (x))

y^{^{'}} = 5 y^{\frac{1}{5}}

\frac{d}{d x} (3 x + \frac{6}{x})

What is the integral of 5t^2e^{(t^3)/3} ?
The integral of 5t^2e^{(t^3)/3} is 5e^{(t^3)/3}+C