What is the integral of 110*(3-ln(x))/(x^2) ?

The integral of 110*(3-ln(x))/(x^2) is 110(-2/x+(ln(x))/x)+C

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integral of 110*(3-ln(x))/(x^2)

\int 110 \cdot \frac{3 - ln ( x )}{x ^{2}} d x

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

Solution steps

\int 110 \cdot \frac{3 - ln ( x )}{x ^{2}} d x

Take the constant out:

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

= 110 \cdot \int \frac{3 - ln ( x )}{x ^{2}} d x

Expand

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

= 110 \cdot \int \frac{3}{x ^{2}} - \frac{ln ( x )}{x ^{2}} 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

= 110 (\int \frac{3}{x ^{2}} d x - \int \frac{ln ( x )}{x ^{2}} d x)

\int \frac{3}{x ^{2}} d x = - \frac{3}{x}

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

= 110 (- \frac{3}{x} - (- \frac{ln ( x )}{x} - \frac{1}{x}))

Expand

- \frac{3}{x} - (- \frac{ln ( x )}{x} - \frac{1}{x}) : - \frac{2}{x} + \frac{ln ( x )}{x}

= 110 (- \frac{2}{x} + \frac{ln ( x )}{x})

Add a constant to the solution

= 110 (- \frac{2}{x} + \frac{ln ( x )}{x}) + C

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What is the integral of 110*(3-ln(x))/(x^2) ?
The integral of 110*(3-ln(x))/(x^2) is 110(-2/x+(ln(x))/x)+C