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

The integral of ln^3(x) is xln^3(x)-3(xln^2(x)-2(xln(x)-x))+C

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integral of ln^3(x)

\int ln^{3} (x) d x

x ln^{3} (x) - 3 (x ln^{2} (x) - 2 (x ln (x) - x)) + C

Solution steps

\int ln^{3} (x) d x

Apply Integration By Parts

: x ln^{3} (x) - \int 3 ln^{2} (x) d x

= x ln^{3} (x) - \int 3 ln^{2} (x) d x

\int 3 ln^{2} (x) d x = 3 (x ln^{2} (x) - 2 (x ln (x) - x))

= x ln^{3} (x) - 3 (x ln^{2} (x) - 2 (x ln (x) - x))

Add a constant to the solution

= x ln^{3} (x) - 3 (x ln^{2} (x) - 2 (x ln (x) - x)) + C

\int \frac{sin ( t )}{cos ^{3} ( t )} d t

x \to - 3 lim (1)

\frac{d}{d x} (x^{3} \cdot cos (x))

\frac{d}{d x} (3 x^{\frac{2}{3}} - 6 x^{\frac{1}{3}} + x^{- \frac{1}{3}})

\frac{d}{d x} (\frac{1}{2} x sin (x))

What is the integral of ln^3(x) ?
The integral of ln^3(x) is xln^3(x)-3(xln^2(x)-2(xln(x)-x))+C