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Popular Calculus >

integral of x^3e-x^2

Solution

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

Solution

\frac{e x ^{4}}{4} - \frac{x ^{3}}{3} + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int x^{3} e d x = \frac{e x ^{4}}{4}

\int x^{2} d x = \frac{x ^{3}}{3}

= \frac{e x ^{4}}{4} - \frac{x ^{3}}{3}

Add a constant to the solution

= \frac{e x ^{4}}{4} - \frac{x ^{3}}{3} + C

Graph

Popular Examples

integral of e^{7x}x

\int e^{7 x} x d x

integral of (2x)/(x^3-x)

\int \frac{2 x}{x ^{3} - x} d x

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\int cot (41 x) d x

integral of (1/x-sin(x))

\int (\frac{1}{x} - sin (x)) d x

integral of (8+2/5 x^2+3/7 x^3)

\int (8 + \frac{2}{5} x^{2} + \frac{3}{7} x^{3}) d x

Frequently Asked Questions (FAQ)

What is the integral of x^3e-x^2 ?
The integral of x^3e-x^2 is (ex^4)/4-(x^3)/3+C