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

The integral of (e^{sqrt(5x+3)})/(sqrt(5x+3)) is 2/5 e^{sqrt(5x+3)}+C

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

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

\frac{2}{5} e^{5 x + 3} + C

Solution steps

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

Apply u-substitution

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

= \int \frac{2}{5} d u

Integral of a constant:

\int a d x = a x

= \frac{2}{5} u

Substitute back

u = e^{5 x + 3}

= \frac{2}{5} e^{5 x + 3}

Add a constant to the solution

= \frac{2}{5} e^{5 x + 3} + C

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What is the integral of (e^{sqrt(5x+3)})/(sqrt(5x+3)) ?
The integral of (e^{sqrt(5x+3)})/(sqrt(5x+3)) is 2/5 e^{sqrt(5x+3)}+C