What is the integral of (5x^2+6+7/(x^2+1)) ?

The integral of (5x^2+6+7/(x^2+1)) is (5x^3)/3+6x+7arctan(x)+C

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integral of (5x^2+6+7/(x^2+1))

\int (5 x^{2} + 6 + \frac{7}{x ^{2} + 1}) d x

\frac{5 x ^{3}}{3} + 6 x + 7 arctan (x) + C

Solution steps

\int 5 x^{2} + 6 + \frac{7}{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 5 x^{2} d x + \int 6 d x + \int \frac{7}{x ^{2} + 1} d x

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

\int 6 d x = 6 x

\int \frac{7}{x ^{2} + 1} d x = 7 arctan (x)

= \frac{5 x ^{3}}{3} + 6 x + 7 arctan (x)

Add a constant to the solution

= \frac{5 x ^{3}}{3} + 6 x + 7 arctan (x) + C

\frac{d}{d x} (- cosh (x))

f (x) = \frac{9}{x ^{2}}, at x = a

n = 2 \sum \infty \frac{1}{n \cdot ( n + 1 )}

f (x) = x^{2} (x^{2} - 8)

(1 + y^{2}) (d x) = x d y

What is the integral of (5x^2+6+7/(x^2+1)) ?
The integral of (5x^2+6+7/(x^2+1)) is (5x^3)/3+6x+7arctan(x)+C