What is the integral of (2+x^2)^2 ?

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

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integral of (2+x^2)^2

\int (2 + x^{2})^{2} d x

4 x + \frac{4 x ^{3}}{3} + \frac{x ^{5}}{5} + C

Solution steps

\int (2 + x^{2})^{2} d x

Expand

(2 + x^{2})^{2} : 4 + 4 x^{2} + x^{4}

= \int 4 + 4 x^{2} + x^{4} 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 d x + \int 4 x^{2} d x + \int x^{4} d x

\int 4 d x = 4 x

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

\int x^{4} d x = \frac{x ^{5}}{5}

= 4 x + \frac{4 x ^{3}}{3} + \frac{x ^{5}}{5}

Add a constant to the solution

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

\frac{\partial}{\partial x} (sin (x y))

\int_{0}^{4} x e^{- x} d x

y = x^{3}, y = 8, x = - 1

x \to 0 lim (2^{x})

2 x^{3} ln (10 x)

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