What is the integral of (-3e^{sqrt(5x)})/(sqrt(5x)) ?

The integral of (-3e^{sqrt(5x)})/(sqrt(5x)) is -6/5 e^{sqrt(5)sqrt(x)}+C

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integral of (-3e^{sqrt(5x)})/(sqrt(5x))

\int \frac{- 3 e ^{5 x}}{5 x} d x

- \frac{6}{5} e^{5 x} + C

Solution steps

\int \frac{- 3 e ^{5 x}}{5 x} d x

Take the constant out:

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

= - 3 \cdot \int \frac{e ^{5 x}}{5 x} d x

Simplify

\frac{e ^{5 x}}{5 x} : \frac{e ^{5 x}}{5 x}

= - 3 \cdot \int \frac{e ^{5 x}}{5 x} d x

Take the constant out:

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

= - 3 \cdot \frac{1}{5} \cdot \int \frac{e ^{5 x}}{x} d x

Apply u-substitution

: \int \frac{2 e ^{u}}{5} d u

= - 3 \cdot \frac{1}{5} \cdot \int \frac{2 e ^{u}}{5} d u

Take the constant out:

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

= - 3 \cdot \frac{1}{5} \cdot \frac{2}{5} \cdot \int e^{u} d u

Use the common integral:

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

= - 3 \cdot \frac{1}{5} \cdot \frac{2}{5} e^{u}

Substitute back

u = 5 x

= - 3 \cdot \frac{1}{5} \cdot \frac{2}{5} e^{5 x}

Simplify

- 3 \cdot \frac{1}{5} \cdot \frac{2}{5} e^{5 x} : - \frac{6}{5} e^{5 x}

= - \frac{6}{5} e^{5 x}

Add a constant to the solution

= - \frac{6}{5} e^{5 x} + C

e^{l n (c o s (x^{2}))} 2 x + 1

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

\int 3 sin (t) cos^{2} (t) d t

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

x \to 3 lim (2 x)

What is the integral of (-3e^{sqrt(5x)})/(sqrt(5x)) ?
The integral of (-3e^{sqrt(5x)})/(sqrt(5x)) is -6/5 e^{sqrt(5)sqrt(x)}+C