What is the integral of 3^{xln(x)}(1+ln(x)) ?

The integral of 3^{xln(x)}(1+ln(x)) is (3^{xln(x)})/(ln(3))+C

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integral of 3^{xln(x)}(1+ln(x))

\int 3^{x l n (x)} (1 + ln (x)) d x

\frac{3 ^{x l n (x)}}{ln ( 3 )} + C

Solution steps

\int 3^{x l n (x)} (1 + ln (x)) d x

Apply u-substitution

: \int 3^{u} d u

= \int 3^{u} d u

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

= \frac{3 ^{u}}{ln ( 3 )}

Substitute back

u = x ln (x)

= \frac{3 ^{x l n (x)}}{ln ( 3 )}

Add a constant to the solution

= \frac{3 ^{x l n (x)}}{ln ( 3 )} + C

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What is the integral of 3^{xln(x)}(1+ln(x)) ?
The integral of 3^{xln(x)}(1+ln(x)) is (3^{xln(x)})/(ln(3))+C