What is the integral of 3x^3e^2x ?

The integral of 3x^3e^2x is (3e^2x^5)/5+C

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integral of 3x^3e^2x

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

\frac{3 e ^{2} x ^{5}}{5} + C

Solution steps

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

Take the constant out:

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

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

Simplify

x^{3} x : x^{4}

= 3 e^{2} \cdot \int x^{4} d x

Apply the Power Rule

: \frac{x ^{5}}{5}

= 3 e^{2} \frac{x ^{5}}{5}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 e ^{2} x ^{5}}{5}

Add a constant to the solution

= \frac{3 e ^{2} x ^{5}}{5} + C

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