What is the integral of e^{x+7e^x} ?

The integral of e^{x+7e^x} is 1/7 e^{7e^x}+C

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integral of e^{x+7e^x}

\int e^{x + 7 e^{x}} d x

\frac{1}{7} e^{7 e^{x}} + C

Solution steps

\int e^{x + 7 e^{x}} d x

Apply u-substitution

: \int e^{7 u} d u

= \int e^{7 u} d u

Apply u-substitution

: \int e^{v} \frac{1}{7} d v

= \int e^{v} \frac{1}{7} d v

Take the constant out:

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

= \frac{1}{7} \cdot \int e^{v} d v

Use the common integral:

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

= \frac{1}{7} e^{v}

Substitute back

= \frac{1}{7} e^{7 e^{x}}

Add a constant to the solution

= \frac{1}{7} e^{7 e^{x}} + C

\frac{d}{d x} (3 x^{2} - 4)

\int - \frac{2}{3} (1 - x)^{\frac{3}{2}} (1) d x

y^{^{''}} + 25 y = sec (5 x)

\int p d p

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 68 y = 0

What is the integral of e^{x+7e^x} ?
The integral of e^{x+7e^x} is 1/7 e^{7e^x}+C