What is the integral of x^4ln(x^5) ?

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

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integral of x^4ln(x^5)

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

x^{5} ln (x) - \frac{x ^{5}}{5} + C

Solution steps

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

Apply Integration By Parts

: \frac{1}{5} x^{5} ln (x^{5}) - \int x^{4} d x

= \frac{1}{5} x^{5} ln (x^{5}) - \int x^{4} d x

\int x^{4} d x = \frac{x ^{5}}{5}

= \frac{1}{5} x^{5} ln (x^{5}) - \frac{x ^{5}}{5}

\frac{1}{5} x^{5} ln (x^{5}) = x^{5} ln (x)

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

Add a constant to the solution

= x^{5} ln (x) - \frac{x ^{5}}{5} + C

\frac{d y}{d x} = 2 y - x y^{2}

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

y = \frac{5}{ln ( x )}

f^{^{''}} (x) = e^{x}

\int x^{3} e^{5 x} d x

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