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

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

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integral of ln(x^5)

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

5 x ln (x) - 5 x + C

Solution steps

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

Apply Integration By Parts

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

\int 5 d x = 5 x

= x ln (x^{5}) - 5 x

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= 5 x ln (x) - 5 x

Add a constant to the solution

= 5 x ln (x) - 5 x + C

\frac{d}{d x} (ln (8 x^{2}))

d er i v a t i v e x^{2} + 4 x - 2

n = 1 \sum \infty 2^{- n} + 3^{- n}

t an g e n t - 9 x^{\frac{1}{3}} + 5, at x = 4

\frac{\partial}{\partial z} (ln (x + z) - yz)