What is the integral of ln(x^7) ?

The integral of ln(x^7) is 7xln(x)-7x+C

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integral of ln(x^7)

\int ln (x^{7}) d x

7 x ln (x) - 7 x + C

Solution steps

\int ln (x^{7}) d x

Apply Integration By Parts

: x ln (x^{7}) - \int 7 d x

= x ln (x^{7}) - \int 7 d x

\int 7 d x = 7 x

= x ln (x^{7}) - 7 x

Apply log rule

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

assuming

x \geq 0

= 7 x ln (x) - 7 x

Add a constant to the solution

= 7 x ln (x) - 7 x + C

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

\int (2 a x + b) (a x^{2} + b x)^{7} d x

\int e^{- 3 x} sin (2 x) d x

x^{2} 5^{x}

\frac{\partial}{\partial x} (ln (8 x^{2} + y^{2} + 3))