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

The integral of e^{sqrt(5x)} is 2/(sqrt(5))e^{sqrt(5)sqrt(x)}sqrt(x)-2/5 e^{sqrt(5)sqrt(x)}+C

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integral of e^{sqrt(5x)}

\int e^{5 x} d x

\frac{2}{5} e^{5 x} x - \frac{2}{5} e^{5 x} + C

Solution steps

\int e^{5 x} d x

Apply Integration By Parts

: e^{5 x} x - \int \frac{5}{2} e^{5 x} x d x

= e^{5 x} x - \int \frac{5}{2} e^{5 x} x d x

\int \frac{5}{2} e^{5 x} x d x = \frac{1}{5} (5 e^{5 x} x - 2 (5 e^{5 x} x - e^{5 x}))

= e^{5 x} x - \frac{1}{5} (5 e^{5 x} x - 2 (5 e^{5 x} x - e^{5 x}))

Simplify

e^{5 x} x - \frac{1}{5} (5 e^{5 x} x - 2 (5 e^{5 x} x - e^{5 x})) : \frac{2}{5} e^{5 x} x - \frac{2}{5} e^{5 x}

= \frac{2}{5} e^{5 x} x - \frac{2}{5} e^{5 x}

Add a constant to the solution

= \frac{2}{5} e^{5 x} x - \frac{2}{5} e^{5 x} + C

\int \frac{x ^{2}}{x + 1} d x

x y^{^{'}} + y = - 7 x y^{2}

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

f (x) = x^{4} e^{x}

y = 4 x^{3} - 20 x + 25

What is the integral of e^{sqrt(5x)} ?
The integral of e^{sqrt(5x)} is 2/(sqrt(5))e^{sqrt(5)sqrt(x)}sqrt(x)-2/5 e^{sqrt(5)sqrt(x)}+C