What is the integral of x^2+ln^5(x) ?

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

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integral of x^2+ln^5(x)

integral

x^{2} + ln^{5} (x)

\frac{x ^{3}}{3} + 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 x^{2} + ln^{5} (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{2} d x + \int ln^{5} (x) d x

\int x^{2} d x = \frac{x ^{3}}{3}

\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))))

= \frac{x ^{3}}{3} + 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

= \frac{x ^{3}}{3} + 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

\frac{1}{( 1 + e ^{- x} )}

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

y = sin^{2} (x)

\frac{1}{( x ^{4} )}

lo g_{10} (\frac{( 1 + x )}{( 1 - x )})

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