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Popular >

integral of x^2ex^3

Solution

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

Solution

\frac{e x ^{6}}{6} + C

Solution steps

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

Take the constant out:

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

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

Simplify

x^{2} x^{3} : x^{5}

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

Apply the Power Rule

: \frac{x ^{6}}{6}

= e \frac{x ^{6}}{6}

Multiply fractions:

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

= \frac{e x ^{6}}{6}

Add a constant to the solution

= \frac{e x ^{6}}{6} + C

Popular Examples

integral of 2(5^x)

\int 2 (5^{x}) d x

integral of 6/(1+2x)

\int \frac{6}{1 + 2 x} d x

integral of x(x-2)^5

\int x (x - 2)^{5} d x

integral of ((3+sqrt(x)+x))/x

\int \frac{( 3 + x + x )}{x} d x

integral of x(x+9)^5

\int x (x + 9)^{5} d x

Frequently Asked Questions (FAQ)

What is the integral of x^2ex^3 ?
The integral of x^2ex^3 is (ex^6)/6+C