What is the integral of (2w-5)/(w^2-3w+9/2) ?

The integral of (2w-5)/(w^2-3w+9/2) is (2(-5+2w))/(9+2w^2-6w)x+C

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integral of (2w-5)/(w^2-3w+9/2)

\int \frac{2 w - 5}{w ^{2} - 3 w + \frac{9}{2}} d x

\frac{2 ( - 5 + 2 w )}{9 + 2 w ^{2} - 6 w} x + C

Solution steps

\int \frac{2 w - 5}{w ^{2} - 3 w + \frac{9}{2}} d x

Integral of a constant:

\int a d x = a x

= \frac{- 5 + 2 w}{\frac{9}{2} + w ^{2} - 3 w} x

\frac{- 5 + 2 w}{\frac{9}{2} + w ^{2} - 3 w} = \frac{2 ( - 5 + 2 w )}{9 + 2 w ^{2} - 6 w}

= \frac{2 ( - 5 + 2 w )}{9 + 2 w ^{2} - 6 w} x

Add a constant to the solution

= \frac{2 ( - 5 + 2 w )}{9 + 2 w ^{2} - 6 w} x + C

2 x + y^{2} = 8, x = y

\frac{\partial}{\partial x} (6 x y - 2 y^{2})

\frac{d}{d x} (\frac{4}{7 x ^{2}})

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

y = \frac{1}{x - 2}

What is the integral of (2w-5)/(w^2-3w+9/2) ?
The integral of (2w-5)/(w^2-3w+9/2) is (2(-5+2w))/(9+2w^2-6w)x+C