What is the integral of 5t^2e^{8t^3} ?

The integral of 5t^2e^{8t^3} is 5/24 e^{8t^3}+C

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integral of 5t^2e^{8t^3}

\int 5 t^{2} e^{8 t^{3}} d t

\frac{5}{24} e^{8 t^{3}} + C

Solution steps

\int 5 t^{2} e^{8 t^{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^{8 t^{3}} d t

Apply u-substitution

: \int \frac{e ^{u}}{24} d u

= 5 \cdot \int \frac{e ^{u}}{24} d u

Take the constant out:

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

= 5 \cdot \frac{1}{24} \cdot \int e^{u} d u

Use the common integral:

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

= 5 \cdot \frac{1}{24} e^{u}

Substitute back

u = 8 t^{3}

= 5 \cdot \frac{1}{24} e^{8 t^{3}}

Simplify

5 \cdot \frac{1}{24} e^{8 t^{3}} : \frac{5}{24} e^{8 t^{3}}

= \frac{5}{24} e^{8 t^{3}}

Add a constant to the solution

= \frac{5}{24} e^{8 t^{3}} + C

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What is the integral of 5t^2e^{8t^3} ?
The integral of 5t^2e^{8t^3} is 5/24 e^{8t^3}+C