What is the integral of (8x-7)*ln(x) ?

The integral of (8x-7)*ln(x) is 8(1/2 x^2ln(x)-(x^2)/4)-7(xln(x)-x)+C

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integral of (8x-7)*ln(x)

\int (8 x - 7) \cdot ln (x) d x

8 (\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}) - 7 (x ln (x) - x) + C

Solution steps

\int (8 x - 7) ln (x) d x

Expand

(8 x - 7) ln (x) : 8 x ln (x) - 7 ln (x)

= \int 8 x ln (x) - 7 ln (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 8 x ln (x) d x - \int 7 ln (x) d x

\int 8 x ln (x) d x = 8 (\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4})

\int 7 ln (x) d x = 7 (x ln (x) - x)

= 8 (\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}) - 7 (x ln (x) - x)

Add a constant to the solution

= 8 (\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}) - 7 (x ln (x) - x) + C

x 8 - 2 x^{2}, 0, 2

\frac{\partial}{\partial x} (ln (\frac{x}{y}))

\int_{- a}^{a} e^{\frac{- x ^{2}}{a ^{2}}} d x

(- 4, 3), (3, 1)

What is the integral of (8x-7)*ln(x) ?
The integral of (8x-7)*ln(x) is 8(1/2 x^2ln(x)-(x^2)/4)-7(xln(x)-x)+C