What is the integral of ln(x^6) ?

The integral of ln(x^6) is 6xln(x)-6x+C

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integral of ln(x^6)

\int ln (x^{6}) d x

6 x ln (x) - 6 x + C

Solution steps

\int ln (x^{6}) d x

Apply Integration By Parts

: x ln (x^{6}) - \int 6 d x

= x ln (x^{6}) - \int 6 d x

\int 6 d x = 6 x

= x ln (x^{6}) - 6 x

Apply log rule

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

assuming

x \geq 0

= 6 x ln (x) - 6 x

Add a constant to the solution

= 6 x ln (x) - 6 x + C

\frac{d y}{d t} = \frac{3 ( y + 1 )}{t ^{2} + 5 t + 6}

\frac{d y}{d x} = \frac{x ^{4} y ^{4} + 4 x ^{4}}{y ^{3}}

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