What is the integral of (5x-7)/(2x^2-3x+7) ?

The integral of (5x-7)/(2x^2-3x+7) is

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integral of (5x-7)/(2x^2-3x+7)

\int \frac{5 x - 7}{2 x ^{2} - 3 x + 7} d x

5 (\frac{3}{2 47} arctan (\frac{1}{47} (4 x - 3)) + \frac{1}{4} ln 16 x^{2} - 24 x + 56) - \frac{14}{47} arctan (\frac{4 x - 3}{47}) + C

Solution steps

\int \frac{5 x - 7}{2 x ^{2} - 3 x + 7} d x

Expand

\frac{5 x - 7}{2 x ^{2} - 3 x + 7} : \frac{5 x}{2 x ^{2} - 3 x + 7} - \frac{7}{2 x ^{2} - 3 x + 7}

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}{2 x ^{2} - 3 x + 7} d x - \int \frac{7}{2 x ^{2} - 3 x + 7} d x

\int \frac{5 x}{2 x ^{2} - 3 x + 7} d x = 5 (\frac{3}{2 47} arctan (\frac{1}{47} (4 x - 3)) + \frac{1}{4} ln 16 x^{2} - 24 x + 56)

\int \frac{7}{2 x ^{2} - 3 x + 7} d x = \frac{14}{47} arctan (\frac{4 x - 3}{47})

= 5 (\frac{3}{2 47} arctan (\frac{1}{47} (4 x - 3)) + \frac{1}{4} ln 16 x^{2} - 24 x + 56) - \frac{14}{47} arctan (\frac{4 x - 3}{47})

Add a constant to the solution

= 5 (\frac{3}{2 47} arctan (\frac{1}{47} (4 x - 3)) + \frac{1}{4} ln 16 x^{2} - 24 x + 56) - \frac{14}{47} arctan (\frac{4 x - 3}{47}) + C

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What is the integral of (5x-7)/(2x^2-3x+7) ?
The integral of (5x-7)/(2x^2-3x+7) is