What is the integral of ((ln(x)+7)^3)/x ?

The integral of ((ln(x)+7)^3)/x is ((ln(x)+7)^4)/4+C

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integral of ((ln(x)+7)^3)/x

\int \frac{( ln ( x ) + 7 ) ^{3}}{x} d x

\frac{( ln ( x ) + 7 ) ^{4}}{4} + C

Solution steps

\int \frac{( ln ( x ) + 7 ) ^{3}}{x} d x

Apply u-substitution

: \int u^{3} d u

= \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= \frac{u ^{4}}{4}

Substitute back

u = ln (x) + 7

= \frac{( ln ( x ) + 7 ) ^{4}}{4}

Add a constant to the solution

= \frac{( ln ( x ) + 7 ) ^{4}}{4} + C

\frac{d}{d x} (3 x^{2} - 4 x + 10)

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

y = x^{3} + x^{2} + x - 1, y = x^{3} + 5

\frac{d y}{d t} = 2 y + y^{5}, y (0) = 1

\frac{- 1}{s + 1}

What is the integral of ((ln(x)+7)^3)/x ?
The integral of ((ln(x)+7)^3)/x is ((ln(x)+7)^4)/4+C