What is the integral of (5x)/(x^2+6)-1 ?

The integral of (5x)/(x^2+6)-1 is 5/2 ln|x^2+6|-x+C

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integral of (5x)/(x^2+6)-1

\int \frac{5 x}{x ^{2} + 6} - 1 d x

\frac{5}{2} ln x^{2} + 6 - x + C

Solution steps

\int \frac{5 x}{x ^{2} + 6} - 1 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

= \int \frac{5 x}{x ^{2} + 6} d x - \int 1 d x

\int \frac{5 x}{x ^{2} + 6} d x = \frac{5}{2} ln x^{2} + 6

\int 1 d x = x

= \frac{5}{2} ln x^{2} + 6 - x

Add a constant to the solution

= \frac{5}{2} ln x^{2} + 6 - x + C

What is the integral of (5x)/(x^2+6)-1 ?
The integral of (5x)/(x^2+6)-1 is 5/2 ln|x^2+6|-x+C