What is the integral of (5x^2+6+9/(x^2+1)) ?

The integral of (5x^2+6+9/(x^2+1)) is (5x^3)/3+6x+9arctan(x)+C

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integral of (5x^2+6+9/(x^2+1))

\int (5 x^{2} + 6 + \frac{9}{x ^{2} + 1}) d x

\frac{5 x ^{3}}{3} + 6 x + 9 arctan (x) + C

Solution steps

\int 5 x^{2} + 6 + \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 5 x^{2} d x + \int 6 d x + \int \frac{9}{x ^{2} + 1} d x

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

\int 6 d x = 6 x

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

= \frac{5 x ^{3}}{3} + 6 x + 9 arctan (x)

Add a constant to the solution

= \frac{5 x ^{3}}{3} + 6 x + 9 arctan (x) + C

\frac{d h}{d t} + \frac{1}{2} h = 1

\int e^{c o s (6 t)} sin (6 t) d t

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = - 4, y^{^{'}} (0) = 4

\int \frac{1}{100 + 2 t} d t

What is the integral of (5x^2+6+9/(x^2+1)) ?
The integral of (5x^2+6+9/(x^2+1)) is (5x^3)/3+6x+9arctan(x)+C