What is the integral of 5e^{2x+e^{2x}} ?

The integral of 5e^{2x+e^{2x}} is 5/2 e^{e^{2x}}+C

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integral of 5e^{2x+e^{2x}}

\int 5 e^{2 x + e^{2 x}} d x

\frac{5}{2} e^{e^{2 x}} + C

Solution steps

\int 5 e^{2 x + e^{2 x}} d x

Take the constant out:

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

= 5 \cdot \int e^{2 x + e^{2 x}} d x

Apply u-substitution

: \int \frac{e ^{u}}{2} d u

= 5 \cdot \int \frac{e ^{u}}{2} d u

Take the constant out:

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

= 5 \cdot \frac{1}{2} \cdot \int e^{u} d u

Use the common integral:

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

= 5 \cdot \frac{1}{2} e^{u}

Substitute back

u = e^{2 x}

= 5 \cdot \frac{1}{2} e^{e^{2 x}}

Simplify

5 \cdot \frac{1}{2} e^{e^{2 x}} : \frac{5}{2} e^{e^{2 x}}

= \frac{5}{2} e^{e^{2 x}}

Add a constant to the solution

= \frac{5}{2} e^{e^{2 x}} + C

\int x^{2} + y^{2} d x

x \to 5 lim (\frac{1}{x})

\frac{d}{d x} (1 + sin (x))

f (x) = \frac{72}{x}

\frac{d}{d x} ((x + 3)^{2})

What is the integral of 5e^{2x+e^{2x}} ?
The integral of 5e^{2x+e^{2x}} is 5/2 e^{e^{2x}}+C