What is the integral of (rivative of 4x)/((x^2-9)) ?

The integral of (rivative of 4x)/((x^2-9)) is (x derivative of 4x)/(x^2-9)-4/(x^2-9)+C

integral of (rivative of 4x)/((x^2-9))

\int \frac{\frac{d}{d x} ( 4 x )}{( x ^{2} - 9 )} d x

\frac{x \frac{d}{d x} ( 4 x )}{x ^{2} - 9} - \frac{4}{x ^{2} - 9} + C

Solution steps

\int \frac{\frac{d}{d x} ( 4 x )}{x ^{2} - 9} d x

Apply Integration By Parts

= \frac{x \frac{d}{d x} ( 4 x )}{x ^{2} - 9} - \int - \frac{8 x}{( x ^{2} - 9 ) ^{2}} d x

\int - \frac{8 x}{( x ^{2} - 9 ) ^{2}} d x = \frac{4}{x ^{2} - 9}

= \frac{x \frac{d}{d x} ( 4 x )}{x ^{2} - 9} - \frac{4}{x ^{2} - 9}

Add a constant to the solution

= \frac{x \frac{d}{d x} ( 4 x )}{x ^{2} - 9} - \frac{4}{x ^{2} - 9} + C

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What is the integral of (rivative of 4x)/((x^2-9)) ?
The integral of (rivative of 4x)/((x^2-9)) is (x derivative of 4x)/(x^2-9)-4/(x^2-9)+C