What is the integral of e^{3x+e^{3x}} ?

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

Popular >

integral of e^{3x+e^{3x}}

\int e^{3 x + e^{3 x}} d x

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

Solution steps

\int e^{3 x + e^{3 x}} d x

Apply u-substitution

: \int e^{u + e^{u}} \frac{1}{3} d u

= \int e^{u + e^{u}} \frac{1}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int e^{u + e^{u}} d u

Apply u-substitution

: \int e^{v} d v

= \frac{1}{3} \cdot \int e^{v} d v

Use the common integral:

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

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

Substitute back

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

Add a constant to the solution

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

\int 5 - y d y

\frac{1}{2 r} + \frac{1}{4 r ^{\frac{3}{4}}}

x

\frac{d}{d x} (\frac{1}{( 2 + x ) ^{2}})

arctan (\frac{x}{2})

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