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

The integral of e^{5x+e^{5x}} is 1/5 e^{e^{5x}}+C

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integral of e^{5x+e^{5x}}

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

\frac{1}{5} e^{e^{5 x}} + C

Solution steps

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

Apply u-substitution

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

= \int e^{u + 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

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

Apply u-substitution

: \int e^{v} d v

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

Use the common integral:

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

= \frac{1}{5} e^{v}

Substitute back

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

Add a constant to the solution

= \frac{1}{5} e^{e^{5 x}} + C

\frac{s}{2 s ^{2} + 4 s + 3}

\frac{d y}{d x} = \frac{x 1 - y ^{2}}{y 1 - x ^{2}}

\int x^{3} - 2 x^{- 2} + 6 x d x

9 + x^{2}

ln (4 x^{3})

What is the integral of e^{5x+e^{5x}} ?
The integral of e^{5x+e^{5x}} is 1/5 e^{e^{5x}}+C