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Popular >

integral of 5xe^3

Solution

\int 5 x e^{3} d x

Solution

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

Solution steps

\int 5 x e^{3} d x

Take the constant out:

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

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

Apply the Power Rule

: \frac{x ^{2}}{2}

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

Multiply fractions:

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

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

Add a constant to the solution

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

Graph

Popular Examples

integral of 9-(x^2)/3

\int 9 - \frac{x ^{2}}{3} d x

integral of sqrt(x/a)

\int \frac{x}{a} d x

integral of 1/((1+289x^2)^{3/2)}

\int \frac{1}{( 1 + 289 x ^{2} ) ^{\frac{3}{2}}} d x

integral of (x+1)(2+x)^7

\int (x + 1) (2 + x)^{7} d x

integral of 2xsqrt(x-7)

\int 2 x x - 7 d x

Frequently Asked Questions (FAQ)

What is the integral of 5xe^3 ?
The integral of 5xe^3 is (5e^3x^2)/2+C