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

The integral of q^5ln(5q) is 1/6 q^6ln(5q)-(q^6)/(36)+C

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integral of q^5ln(5q)

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

\frac{1}{6} q^{6} ln (5 q) - \frac{q ^{6}}{36} + C

Solution steps

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

Apply Integration By Parts

: \frac{1}{6} q^{6} ln (5 q) - \int \frac{q ^{5}}{6} d q

= \frac{1}{6} q^{6} ln (5 q) - \int \frac{q ^{5}}{6} d q

\int \frac{q ^{5}}{6} d q = \frac{q ^{6}}{36}

= \frac{1}{6} q^{6} ln (5 q) - \frac{q ^{6}}{36}

Add a constant to the solution

= \frac{1}{6} q^{6} ln (5 q) - \frac{q ^{6}}{36} + C

\frac{d}{d x} (ln (x^{y}))

\int u^{- 2} (2 u^{4} + 3 u^{2} - 2 u^{- 3}) d u

\frac{d}{d x} (\frac{3 x - 4}{2 x ^{2} + 5})

\frac{d}{d x} (x^{2} e^{- 2 x})

What is the integral of q^5ln(5q) ?
The integral of q^5ln(5q) is 1/6 q^6ln(5q)-(q^6)/(36)+C