What is the integral of 2x^2+7+9/(x^2+1) ?

The integral of 2x^2+7+9/(x^2+1) is (2x^3)/3+7x+9arctan(x)+C

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integral of 2x^2+7+9/(x^2+1)

\int 2 x^{2} + 7 + \frac{9}{x ^{2} + 1} d x

\frac{2 x ^{3}}{3} + 7 x + 9 arctan (x) + C

Solution steps

\int 2 x^{2} + 7 + \frac{9}{x ^{2} + 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 2 x^{2} d x + \int 7 d x + \int \frac{9}{x ^{2} + 1} d x

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

\int 7 d x = 7 x

\int \frac{9}{x ^{2} + 1} d x = 9 arctan (x)

= \frac{2 x ^{3}}{3} + 7 x + 9 arctan (x)

Add a constant to the solution

= \frac{2 x ^{3}}{3} + 7 x + 9 arctan (x) + C

\frac{d}{d x} ((ln (x))^{3})

\frac{\partial}{\partial x} (\frac{1}{x - b})

f (x) = \frac{( 10 - 3 x ) + 2}{2}

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

\int \frac{I n ( 3 x )}{2 x} d x

What is the integral of 2x^2+7+9/(x^2+1) ?
The integral of 2x^2+7+9/(x^2+1) is (2x^3)/3+7x+9arctan(x)+C