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{d}{d x} (e^{x} + 2)

\frac{( x + 1 ) d y}{d x} (x + 1) y = 2 x e^{- x}

\int \frac{x ^{3}}{( x ^{2} + 12 ) ^{3}} d x

\frac{d y}{d x} = \frac{1}{x ^{2} y ^{2}}

x^{2} e^{4 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