What is the integral of e^{6x+e^{6x}} ?

The integral of e^{6x+e^{6x}} is 1/6 e^{e^{6x}}+C

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integral of e^{6x+e^{6x}}

\int e^{6 x + e^{6 x}} d x

\frac{1}{6} e^{e^{6 x}} + C

Solution steps

\int e^{6 x + e^{6 x}} d x

Apply u-substitution

: \int e^{u + e^{u}} \frac{1}{6} d u

= \int e^{u + e^{u}} \frac{1}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int e^{u + e^{u}} d u

Apply u-substitution

: \int e^{v} d v

= \frac{1}{6} \cdot \int e^{v} d v

Use the common integral:

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

= \frac{1}{6} e^{v}

Substitute back

= \frac{1}{6} e^{e^{6 x}}

Add a constant to the solution

= \frac{1}{6} e^{e^{6 x}} + C

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What is the integral of e^{6x+e^{6x}} ?
The integral of e^{6x+e^{6x}} is 1/6 e^{e^{6x}}+C