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

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

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integral of-4ln(x)

integral

- 4 ln (x)

- 4 (x ln (x) - x) + C

Solution steps

\int - 4 ln (x) d x

Take the constant out:

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

= - 4 \cdot \int ln (x) d x

Apply Integration By Parts

: x ln (x) - \int 1 d x

= - 4 (x ln (x) - \int 1 d x)

\int 1 d x = x

= - 4 (x ln (x) - x)

Add a constant to the solution

= - 4 (x ln (x) - x) + C

\frac{1}{( x ( x - 1 ) )}

e^{x} \cdot (\frac{1}{x})

\frac{1}{( 3 t ^{4} + 4 t ^{2} + 1 )}

\frac{( x - 2 ) ^{3}}{3 x ^{2}}

\frac{t ^{3}}{( 1 + t ^{6} )}