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Popular >

integral of e^5x

Solution

\int e^{5} x d x

Solution

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

Solution steps

\int e^{5} x d x

Take the constant out:

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

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

Apply the Power Rule

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

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

Multiply fractions:

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

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

Add a constant to the solution

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

Popular Examples

integral of (3x+10)/(x^2+2x)

\int \frac{3 x + 10}{x ^{2} + 2 x} d x

integral of x/(sin^2(x)cos^2(x))

\int \frac{x}{sin ^{2} ( x ) cos ^{2} ( x )} d x

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

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

integral of 1/(7x-9)

\int \frac{1}{7 x - 9} d x

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

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

Frequently Asked Questions (FAQ)

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