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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int e^{u + e^{u}} \frac{1}{7} d u

= \int e^{u + e^{u}} \frac{1}{7} d u

Take the constant out:

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

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

Apply u-substitution

: \int e^{v} d v

= \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^{e^{7 x}}

Add a constant to the solution

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

f (x) = 4 x^{3} + 3 x^{2} - 2

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

\int (2 x + 3) e^{0.5 x} d x

f (x) = x^{\frac{2}{7}}

x \to \infty lim (2 x^{2} - 6)

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