What is the integral of-7t^2e^{4t^3} ?

The integral of-7t^2e^{4t^3} is -7/12 e^{4t^3}+C

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integral of-7t^2e^{4t^3}

\int - 7 t^{2} e^{4 t^{3}} d t

- \frac{7}{12} e^{4 t^{3}} + C

Solution steps

\int - 7 t^{2} e^{4 t^{3}} d t

Take the constant out:

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

= - 7 \cdot \int t^{2} e^{4 t^{3}} d t

Apply u-substitution

: \int \frac{e ^{u}}{12} d u

= - 7 \cdot \int \frac{e ^{u}}{12} d u

Take the constant out:

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

= - 7 \cdot \frac{1}{12} \cdot \int e^{u} d u

Use the common integral:

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

= - 7 \cdot \frac{1}{12} e^{u}

Substitute back

u = 4 t^{3}

= - 7 \cdot \frac{1}{12} e^{4 t^{3}}

Simplify

- 7 \cdot \frac{1}{12} e^{4 t^{3}} : - \frac{7}{12} e^{4 t^{3}}

= - \frac{7}{12} e^{4 t^{3}}

Add a constant to the solution

= - \frac{7}{12} e^{4 t^{3}} + C

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What is the integral of-7t^2e^{4t^3} ?
The integral of-7t^2e^{4t^3} is -7/12 e^{4t^3}+C