What is the integral of (3x^2+11v)/(v^2-v-6) ?

The integral of (3x^2+11v)/(v^2-v-6) is 1/(-6-v+v^2)(11vx+x^3)+C

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integral of (3x^2+11v)/(v^2-v-6)

\int \frac{3 x ^{2} + 11 v}{v ^{2} - v - 6}

\frac{1}{- 6 - v + v ^{2}} (11 vx + x^{3}) + C

Solution steps

\int \frac{3 x ^{2} + 11 v}{v ^{2} - v - 6} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{- 6 - v + v ^{2}} \cdot \int 11 v + 3 x^{2} 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

= \frac{1}{- 6 - v + v ^{2}} (\int 11 v d x + \int 3 x^{2} d x)

\int 11 v d x = 11 vx

\int 3 x^{2} d x = x^{3}

= \frac{1}{- 6 - v + v ^{2}} (11 vx + x^{3})

Add a constant to the solution

= \frac{1}{- 6 - v + v ^{2}} (11 vx + x^{3}) + C

\int (2 x^{2} + 3) e^{6 x} d x

\frac{d}{d x} (\frac{4 x ^{3} - 5}{x ^{2} - 3})

x \to 0 - lim (\frac{6}{x})

\frac{d}{d x} (4 x x)

\int \frac{6}{6 x + 1} d x

What is the integral of (3x^2+11v)/(v^2-v-6) ?
The integral of (3x^2+11v)/(v^2-v-6) is 1/(-6-v+v^2)(11vx+x^3)+C