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Popular >

integral of ln^4(x)

Solution

\int ln^{4} (x) d x

Solution

x ln^{4} (x) - 4 (x ln^{3} (x) - 3 (x ln^{2} (x) - 2 (x ln (x) - x))) + C

Solution steps

\int ln^{4} (x) d x

Apply Integration By Parts

: x ln^{4} (x) - \int 4 ln^{3} (x) d x

= x ln^{4} (x) - \int 4 ln^{3} (x) d x

\int 4 ln^{3} (x) d x = 4 (x ln^{3} (x) - 3 (x ln^{2} (x) - 2 (x ln (x) - x)))

= x ln^{4} (x) - 4 (x ln^{3} (x) - 3 (x ln^{2} (x) - 2 (x ln (x) - x)))

Add a constant to the solution

= x ln^{4} (x) - 4 (x ln^{3} (x) - 3 (x ln^{2} (x) - 2 (x ln (x) - x))) + C

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\int 6 x d x

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\int (x^{2} + 1) e^{x^{3} + 3 x} d x

Frequently Asked Questions (FAQ)

What is the integral of ln^4(x) ?
The integral of ln^4(x) is xln^4(x)-4(xln^3(x)-3(xln^2(x)-2(xln(x)-x)))+C