What is the integral of-1ln(2/5 x) ?

The integral of-1ln(2/5 x) is -xln(2/5 x)+x+C

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integral of-1ln(2/5 x)

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

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

Solution steps

\int - 1 \cdot ln (\frac{2}{5} x) d x

Take the constant out:

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

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

Apply Integration By Parts

: x ln (\frac{2}{5} x) - \int 1 d x

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

\int 1 d x = x

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

Simplify

= - x ln (\frac{2}{5} x) + x

Add a constant to the solution

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

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What is the integral of-1ln(2/5 x) ?
The integral of-1ln(2/5 x) is -xln(2/5 x)+x+C