What is the integral of ((3x-17))/((x^2-6x+10)) ?

The integral of ((3x-17))/((x^2-6x+10)) is 3/2 ln|x^2-6x+10|-8arctan(x-3)+C

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integral of ((3x-17))/((x^2-6x+10))

\int \frac{( 3 x - 17 )}{( x ^{2} - 6 x + 10 )} d x

\frac{3}{2} ln x^{2} - 6 x + 10 - 8 arctan (x - 3) + C

Solution steps

\int \frac{3 x - 17}{x ^{2} - 6 x + 10} d x

Apply Integration By Parts

: (3 x - 17) arctan (x - 3) - \int 3 arctan (x - 3) d x

= (3 x - 17) arctan (x - 3) - \int 3 arctan (x - 3) d x

\int 3 arctan (x - 3) d x = 3 (x arctan (x - 3) - \frac{1}{2} ln x^{2} - 6 x + 10 - 3 arctan (x - 3))

= (3 x - 17) arctan (x - 3) - 3 (x arctan (x - 3) - \frac{1}{2} ln x^{2} - 6 x + 10 - 3 arctan (x - 3))

Simplify

(3 x - 17) arctan (x - 3) - 3 (x arctan (x - 3) - \frac{1}{2} ln x^{2} - 6 x + 10 - 3 arctan (x - 3)) : \frac{3}{2} ln x^{2} - 6 x + 10 - 8 arctan (x - 3)

= \frac{3}{2} ln x^{2} - 6 x + 10 - 8 arctan (x - 3)

Add a constant to the solution

= \frac{3}{2} ln x^{2} - 6 x + 10 - 8 arctan (x - 3) + C

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What is the integral of ((3x-17))/((x^2-6x+10)) ?
The integral of ((3x-17))/((x^2-6x+10)) is 3/2 ln|x^2-6x+10|-8arctan(x-3)+C