What is the integral of ln^5(x) ?

The integral of ln^5(x) is xln^5(x)-5(xln^4(x)-4(xln^3(x)-3(xln^2(x)-2(xln(x)-x))))+C

Popular >

integral of ln^5(x)

\int ln^{5} (x) d x

x ln^{5} (x) - 5 (x ln^{4} (x) - 4 (x ln^{3} (x) - 3 (x ln^{2} (x) - 2 (x ln (x) - x)))) + C

Solution steps

\int ln^{5} (x) d x

Apply Integration By Parts

: x ln^{5} (x) - \int 5 ln^{4} (x) d x

= x ln^{5} (x) - \int 5 ln^{4} (x) d x

\int 5 ln^{4} (x) d x = 5 (x ln^{4} (x) - 4 (x ln^{3} (x) - 3 (x ln^{2} (x) - 2 (x ln (x) - x))))

= x ln^{5} (x) - 5 (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^{5} (x) - 5 (x ln^{4} (x) - 4 (x ln^{3} (x) - 3 (x ln^{2} (x) - 2 (x ln (x) - x)))) + C

x \to 10 + lim (\frac{1}{( x - 10 ) ^{2}})

\int_{- 5}^{5} (x - 25 - x^{2}) d x

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

cos (t) y^{^{'}} + sin (t) y - 1 = 0

f (x) = 2 x, (1, 2)

What is the integral of ln^5(x) ?
The integral of ln^5(x) is xln^5(x)-5(xln^4(x)-4(xln^3(x)-3(xln^2(x)-2(xln(x)-x))))+C