What is the integral of e^{x+4e^x} ?

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

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integral of e^{x+4e^x}

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

\frac{1}{4} e^{4 e^{x}} + C

Solution steps

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

Apply u-substitution

: \int e^{4 u} d u

= \int e^{4 u} d u

Apply u-substitution

: \int e^{v} \frac{1}{4} d v

= \int e^{v} \frac{1}{4} d v

Take the constant out:

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

= \frac{1}{4} \cdot \int e^{v} d v

Use the common integral:

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

= \frac{1}{4} e^{v}

Substitute back

= \frac{1}{4} e^{4 e^{x}}

Add a constant to the solution

= \frac{1}{4} e^{4 e^{x}} + C

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