What is the integral of (a^{ln(x)})/x ?

The integral of (a^{ln(x)})/x is (a^{ln(x)})/(ln(a))+C

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integral of (a^{ln(x)})/x

\int \frac{a ^{l n (x)}}{x} d x

\frac{a ^{l n (x)}}{ln ( a )} + C

Solution steps

\int \frac{a ^{l n (x)}}{x} d x

Apply u-substitution

: \int a^{u} d u

= \int a^{u} d u

\int a^{x} d x = \frac{a ^{x}}{ln a}

= \frac{a ^{u}}{ln ( a )}

Substitute back

u = ln (x)

= \frac{a ^{l n (x)}}{ln ( a )}

Add a constant to the solution

= \frac{a ^{l n (x)}}{ln ( a )} + C

\frac{1}{1 - 5 x ^{2}}

\frac{d}{d x} (- 2 x)

\int \frac{1}{( x ^{2} - 1 ) ^{3}} d x

y^{^{''}} + \frac{14}{t} y^{^{'}} + \frac{42}{t ^{2}} y = 0

\frac{d ^{2}}{d x ^{2}} (3^{x})

What is the integral of (a^{ln(x)})/x ?
The integral of (a^{ln(x)})/x is (a^{ln(x)})/(ln(a))+C