What is the integral of ((7e^{7sqrt(x)}))/(sqrt(x)) ?

The integral of ((7e^{7sqrt(x)}))/(sqrt(x)) is 2e^{7sqrt(x)}+C

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integral of ((7e^{7sqrt(x)}))/(sqrt(x))

\int \frac{( 7 e ^{7 x} )}{x} d x

2 e^{7 x} + C

Solution steps

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

Take the constant out:

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

= 7 \cdot \int \frac{e ^{7 x}}{x} d x

Apply u-substitution

: \int \frac{2 e ^{u}}{7} d u

= 7 \cdot \int \frac{2 e ^{u}}{7} d u

Take the constant out:

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

= 7 \cdot \frac{2}{7} \cdot \int e^{u} d u

Use the common integral:

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

= 7 \cdot \frac{2}{7} e^{u}

Substitute back

u = 7 x

= 7 \cdot \frac{2}{7} e^{7 x}

Simplify

7 \cdot \frac{2}{7} e^{7 x} : 2 e^{7 x}

= 2 e^{7 x}

Add a constant to the solution

= 2 e^{7 x} + C

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What is the integral of ((7e^{7sqrt(x)}))/(sqrt(x)) ?
The integral of ((7e^{7sqrt(x)}))/(sqrt(x)) is 2e^{7sqrt(x)}+C