What is the integral of ((ln(x)+7)^{13})/x ?

The integral of ((ln(x)+7)^{13})/x is ((ln(x)+7)^{14})/(14)+C

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integral of ((ln(x)+7)^{13})/x

\int \frac{( ln ( x ) + 7 ) ^{13}}{x} d x

\frac{( ln ( x ) + 7 ) ^{14}}{14} + C

Solution steps

\int \frac{( ln ( x ) + 7 ) ^{13}}{x} d x

Apply u-substitution

: \int u^{13} d u

= \int u^{13} d u

Apply the Power Rule

: \frac{u ^{14}}{14}

= \frac{u ^{14}}{14}

Substitute back

u = ln (x) + 7

= \frac{( ln ( x ) + 7 ) ^{14}}{14}

Add a constant to the solution

= \frac{( ln ( x ) + 7 ) ^{14}}{14} + C

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What is the integral of ((ln(x)+7)^{13})/x ?
The integral of ((ln(x)+7)^{13})/x is ((ln(x)+7)^{14})/(14)+C