What is the integral of (3x^2e^{x^3-1}) ?

The integral of (3x^2e^{x^3-1}) is e^{x^3-1}+C

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integral of (3x^2e^{x^3-1})

\int (3 x^{2} e^{x^{3} - 1}) d x

e^{x^{3} - 1} + C

Solution steps

\int 3 x^{2} e^{x^{3} - 1} d x

Take the constant out:

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

= 3 \cdot \int x^{2} e^{x^{3} - 1} d x

Apply u-substitution

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

= 3 \cdot \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

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

Use the common integral:

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

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

Substitute back

u = x^{3} - 1

= 3 \cdot \frac{1}{3} e^{x^{3} - 1}

Simplify

3 \cdot \frac{1}{3} e^{x^{3} - 1} : e^{x^{3} - 1}

= e^{x^{3} - 1}

Add a constant to the solution

= e^{x^{3} - 1} + C

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What is the integral of (3x^2e^{x^3-1}) ?
The integral of (3x^2e^{x^3-1}) is e^{x^3-1}+C