What is the integral of (4x^2+3+5/(x^2+1)) ?

The integral of (4x^2+3+5/(x^2+1)) is (4x^3)/3+3x+5arctan(x)+C

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integral of (4x^2+3+5/(x^2+1))

\int (4 x^{2} + 3 + \frac{5}{x ^{2} + 1}) d x

\frac{4 x ^{3}}{3} + 3 x + 5 arctan (x) + C

Solution steps

\int 4 x^{2} + 3 + \frac{5}{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 4 x^{2} d x + \int 3 d x + \int \frac{5}{x ^{2} + 1} d x

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

\int 3 d x = 3 x

\int \frac{5}{x ^{2} + 1} d x = 5 arctan (x)

= \frac{4 x ^{3}}{3} + 3 x + 5 arctan (x)

Add a constant to the solution

= \frac{4 x ^{3}}{3} + 3 x + 5 arctan (x) + C

\int_{3}^{4} 5 x d x

y^{^{''}} + 9 y = 18

n = 1 \sum \infty \frac{15 n !}{n ^{n}}

\frac{\partial}{\partial x} (2 x + 3 y + 6 x y e^{3 x^{2} y})

\frac{\partial}{\partial x} (x^{2} + x e^{2 y})

What is the integral of (4x^2+3+5/(x^2+1)) ?
The integral of (4x^2+3+5/(x^2+1)) is (4x^3)/3+3x+5arctan(x)+C