What is the integral of x^6ln(2x) ?

The integral of x^6ln(2x) is 1/7 x^7ln(2x)-(x^7)/(49)+C

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integral of x^6ln(2x)

\int x^{6} ln (2 x) d x

\frac{1}{7} x^{7} ln (2 x) - \frac{x ^{7}}{49} + C

Solution steps

\int x^{6} ln (2 x) d x

Apply Integration By Parts

: \frac{1}{7} x^{7} ln (2 x) - \int \frac{x ^{6}}{7} d x

= \frac{1}{7} x^{7} ln (2 x) - \int \frac{x ^{6}}{7} d x

\int \frac{x ^{6}}{7} d x = \frac{x ^{7}}{49}

= \frac{1}{7} x^{7} ln (2 x) - \frac{x ^{7}}{49}

Add a constant to the solution

= \frac{1}{7} x^{7} ln (2 x) - \frac{x ^{7}}{49} + C

\frac{d y}{d t} = 3 y + y^{6}

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

e^{x} \cdot cos (x)

\int_{- 1}^{1} (\frac{1}{1 + x ^{2}})^{2} d x

\int \frac{3 x ^{3} - 4 x ^{2} + 3 x}{x ^{2} + 1} d x

What is the integral of x^6ln(2x) ?
The integral of x^6ln(2x) is 1/7 x^7ln(2x)-(x^7)/(49)+C