What is the integral of-ln(x)-(ln(x))/4 ?

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

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integral of-ln(x)-(ln(x))/4

\int - ln (x) - \frac{ln ( x )}{4} d x

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

Solution steps

\int - ln (x) - \frac{ln ( x )}{4} 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 ln (x) d x - \int \frac{ln ( x )}{4} d x

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

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

= - (x ln (x) - x) - \frac{1}{4} (x ln (x) - x)

Simplify

- (x ln (x) - x) - \frac{1}{4} (x ln (x) - x) : - \frac{5}{4} (x ln (x) - x)

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

Add a constant to the solution

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

\int_{- 2}^{4} t^{2} - 2 t - 3 d t

f^{^{'}} (x) = 2 x^{2} + 3 x - 2

\frac{\partial}{\partial x} (x^{4} y - x^{2} y^{3})

y = 3 x^{2} + \frac{4 x}{3} - 2

\frac{3}{r ^{3}}

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