What is the integral of (8x-3)*ln(x) ?

The integral of (8x-3)*ln(x) is 8(1/2 x^2ln(x)-(x^2)/4)-3(xln(x)-x)+C

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integral of (8x-3)*ln(x)

\int (8 x - 3) \cdot ln (x) d x

8 (\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}) - 3 (x ln (x) - x) + C

Solution steps

\int (8 x - 3) ln (x) d x

Expand

(8 x - 3) ln (x) : 8 x ln (x) - 3 ln (x)

= \int 8 x ln (x) - 3 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 3 ln (x) d x

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

\int 3 ln (x) d x = 3 (x ln (x) - x)

= 8 (\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}) - 3 (x ln (x) - x)

Add a constant to the solution

= 8 (\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}) - 3 (x ln (x) - x) + C

\int \frac{1 - sin ^{2} ( x )}{cos ( x )} d x

(7.7) (2.1)

\frac{t ^{2} e ^{- 2 t}}{2}

\int \frac{1}{u ^{2} - 3} d u

\frac{d}{d x} (\frac{x + 8}{3})

What is the integral of (8x-3)*ln(x) ?
The integral of (8x-3)*ln(x) is 8(1/2 x^2ln(x)-(x^2)/4)-3(xln(x)-x)+C