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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int e^{3 u} d u

= \int e^{3 u} d u

Apply u-substitution

: \int e^{v} \frac{1}{3} d v

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

Take the constant out:

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

= \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^{3 e^{x}}

Add a constant to the solution

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

\frac{d ^{2} y}{d x ^{2}} - 9 y = 0

\frac{\partial}{\partial x} (a - b x - \frac{c}{y} + d \frac{x}{y})

x \to 2 lim (2 x^{2} - x + 2)

(x - y) d x + (x) d y = 0

y^{^{'}} + 3 y = e^{2 x} + 1

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