What is the integral of 2x^3e^{4+1} ?

The integral of 2x^3e^{4+1} is (e^5x^4)/2+C

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integral of 2x^3e^{4+1}

\int 2 x^{3} e^{4 + 1} d x

\frac{e ^{5} x ^{4}}{2} + C

Solution steps

\int 2 x^{3} e^{4 + 1} d x

Take the constant out:

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

= 2 e^{4 + 1} \cdot \int x^{3} d x

Simplify

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

Apply the Power Rule

= 2 e^{5} \frac{x ^{4}}{4}

Simplify

2 e^{5} \frac{x ^{4}}{4} : \frac{e ^{5} x ^{4}}{2}

= \frac{e ^{5} x ^{4}}{2}

Add a constant to the solution

= \frac{e ^{5} x ^{4}}{2} + C

What is the integral of 2x^3e^{4+1} ?
The integral of 2x^3e^{4+1} is (e^5x^4)/2+C