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Popular >

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

Popular Examples

integral of 1/(x^{5/6)}

\int \frac{1}{x ^{\frac{5}{6}}} d x

integral of t^2sqrt(1+4t^2)

\int t^{2} 1 + 4 t^{2} d t

integral of (36-x^2)

\int (36 - x^{2}) d x

integral of 3x^4-5/(x^2)+6

\int 3 x^{4} - \frac{5}{x ^{2}} + 6 d x

integral of e-2x

\int e - 2 x 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