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

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

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integral of e^{sqrt(7x)}

\int e^{7 x} d x

\frac{2}{7} e^{7 x} x - \frac{2}{7} e^{7 x} + C

Solution steps

\int e^{7 x} d x

Apply Integration By Parts

: e^{7 x} x - \int \frac{7}{2} e^{7 x} x d x

= e^{7 x} x - \int \frac{7}{2} e^{7 x} x d x

\int \frac{7}{2} e^{7 x} x d x = \frac{1}{7} (7 e^{7 x} x - 2 (7 e^{7 x} x - e^{7 x}))

= e^{7 x} x - \frac{1}{7} (7 e^{7 x} x - 2 (7 e^{7 x} x - e^{7 x}))

Simplify

e^{7 x} x - \frac{1}{7} (7 e^{7 x} x - 2 (7 e^{7 x} x - e^{7 x})) : \frac{2}{7} e^{7 x} x - \frac{2}{7} e^{7 x}

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

Add a constant to the solution

= \frac{2}{7} e^{7 x} x - \frac{2}{7} e^{7 x} + C

\frac{d}{d x} (x e)

f (x) = 13 x

f (x) = 10 x, at x = 10

y = - x^{2} + 5 x + 2, y = 2

\frac{d}{d x} (\frac{( x ^{2} + 2 x - 5 )}{( x + 1 ) ^{2}})

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