What is the integral of (e^{4x})/(e^x) ?

The integral of (e^{4x})/(e^x) is 1/3 e^{3x}+C

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integral of (e^{4x})/(e^x)

\int \frac{e ^{4 x}}{e ^{x}} d x

\frac{1}{3} e^{3 x} + C

Solution steps

\int \frac{e ^{4 x}}{e ^{x}} d x

Apply u-substitution

: \int \frac{1}{4 4 u} d u

= \int \frac{1}{4 4 u} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int \frac{1}{4 u} d u

Apply the Power Rule

: \frac{4}{3} u^{\frac{3}{4}}

= \frac{1}{4} \cdot \frac{4}{3} u^{\frac{3}{4}}

Substitute back

u = e^{4 x}

= \frac{1}{4} \cdot \frac{4}{3} (e^{4 x})^{\frac{3}{4}}

Simplify

\frac{1}{4} \cdot \frac{4}{3} (e^{4 x})^{\frac{3}{4}} : \frac{1}{3} e^{3 x}

= \frac{1}{3} e^{3 x}

Add a constant to the solution

= \frac{1}{3} e^{3 x} + C

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What is the integral of (e^{4x})/(e^x) ?
The integral of (e^{4x})/(e^x) is 1/3 e^{3x}+C