What is the integral of log_{10}(2/y) ?

The integral of log_{10}(2/y) is ylog_{10}(2/y)+1/(ln(10))y+C

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integral of log_{10}(2/y)

integral

lo g_{10} (\frac{2}{y})

y lo g_{10} (\frac{2}{y}) + \frac{1}{ln ( 10 )} y + C

Solution steps

\int lo g_{10} (\frac{2}{y}) d y

Apply Integration By Parts

: y lo g_{10} (\frac{2}{y}) - \int - \frac{1}{ln ( 10 )} d y

= y lo g_{10} (\frac{2}{y}) - \int - \frac{1}{ln ( 10 )} d y

\int - \frac{1}{ln ( 10 )} d y = - \frac{1}{ln ( 10 )} y

= y lo g_{10} (\frac{2}{y}) - (- \frac{1}{ln ( 10 )} y)

Simplify

= y lo g_{10} (\frac{2}{y}) + \frac{1}{ln ( 10 )} y

Add a constant to the solution

= y lo g_{10} (\frac{2}{y}) + \frac{1}{ln ( 10 )} y + C

\frac{1}{( x ^{5} + x ^{3} )}

t + 2

t + 3

x^{3} - 2 x + 5

\frac{sin ( x )}{4}

What is the integral of log_{10}(2/y) ?
The integral of log_{10}(2/y) is ylog_{10}(2/y)+1/(ln(10))y+C