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

The integral of e^{5sqrt(x)} is 2/25 (e^{5sqrt(x)}*5sqrt(x)-e^{5sqrt(x)})+C

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integral of e^{5sqrt(x)}

\int e^{5 x} d x

\frac{2}{25} (e^{5 x} \cdot 5 x - e^{5 x}) + C

Solution steps

\int e^{5 x} d x

Apply u-substitution

: \int \frac{2 e ^{u} u}{25} d u

= \int \frac{2 e ^{u} u}{25} d u

Take the constant out:

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

= \frac{2}{25} \cdot \int e^{u} u d u

Apply Integration By Parts

: e^{u} u - \int e^{u} d u

= \frac{2}{25} (e^{u} u - \int e^{u} d u)

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

= \frac{2}{25} (e^{u} u - e^{u})

Substitute back

u = 5 x

= \frac{2}{25} (e^{5 x} \cdot 5 x - e^{5 x})

Add a constant to the solution

= \frac{2}{25} (e^{5 x} \cdot 5 x - e^{5 x}) + C

n = 0 \sum \infty 1 + n

\int \frac{5 x}{x ^{4} - 16} d x

\frac{d}{d x} (2 e^{4 x})

y^{^{''}} + 2 y^{^{'}} = - 8

(x + 1) y^{^{'}} = - 2 y + (x + 1)^{\frac{5}{2}}, y (0) = \frac{11}{9}

What is the integral of e^{5sqrt(x)} ?
The integral of e^{5sqrt(x)} is 2/25 (e^{5sqrt(x)}*5sqrt(x)-e^{5sqrt(x)})+C