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Popular >

integral of e^{5x}5

Solution

\int e^{5 x} 5 d x

Solution

e^{5 x} + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int e^{u} \frac{1}{5} d u

= 5 \cdot \int e^{u} \frac{1}{5} d u

Take the constant out:

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

= 5 \cdot \frac{1}{5} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= 5 \cdot \frac{1}{5} e^{u}

Substitute back

u = 5 x

= 5 \cdot \frac{1}{5} e^{5 x}

Simplify

5 \cdot \frac{1}{5} e^{5 x} : e^{5 x}

= e^{5 x}

Add a constant to the solution

= e^{5 x} + C

Graph

Popular Examples

integral of (x^2+5)/x

\int \frac{x ^{2} + 5}{x} d x

integral of 1/Q

\int \frac{1}{Q} d Q

integral of 2e^{-x}cos(5x)

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

integral of 1/(5\sqrt[3]{x^5)}

\int \frac{1}{5 3 x ^{5}} d x

integral of x^3sqrt(x^4+7)

\int x^{3} x^{4} + 7 d x

Frequently Asked Questions (FAQ)

What is the integral of e^{5x}5 ?
The integral of e^{5x}5 is e^{5x}+C