What is the integral of (5^x)/x ?

The integral of (5^x)/x is \Ei(ln(5^x))+C

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integral of (5^x)/x

\int \frac{5 ^{x}}{x} d x

Ei (ln (5^{x})) + C

Solution steps

\int \frac{5 ^{x}}{x} d x

Apply u-substitution

: \int \frac{1}{ln ( u )} d u

= \int \frac{1}{ln ( u )} d u

Apply u-substitution

: \int \frac{e ^{v}}{v} d v

= \int \frac{e ^{v}}{v} d v

Use the nonelementary integral:

\int \frac{e ^{x}}{x} d x = Ei (x)

= Ei (v)

Substitute back

= Ei (ln (5^{x}))

Add a constant to the solution

= Ei (ln (5^{x})) + C

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