What is the integral of 5xln(x^7) ?

The integral of 5xln(x^7) is 5(7/2 x^2ln(x)-(7x^2)/4)+C

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integral of 5xln(x^7)

\int 5 x ln (x^{7}) d x

5 (\frac{7}{2} x^{2} ln (x) - \frac{7 x ^{2}}{4}) + C

Solution steps

\int 5 x ln (x^{7}) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int x ln (x^{7}) d x

Apply Integration By Parts

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

= 5 (\frac{1}{2} x^{2} ln (x^{7}) - \int \frac{7 x}{2} d x)

\int \frac{7 x}{2} d x = \frac{7 x ^{2}}{4}

= 5 (\frac{1}{2} x^{2} ln (x^{7}) - \frac{7 x ^{2}}{4})

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

= 5 (\frac{7}{2} x^{2} ln (x) - \frac{7 x ^{2}}{4})

Add a constant to the solution

= 5 (\frac{7}{2} x^{2} ln (x) - \frac{7 x ^{2}}{4}) + C

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What is the integral of 5xln(x^7) ?
The integral of 5xln(x^7) is 5(7/2 x^2ln(x)-(7x^2)/4)+C