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

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

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integral of (x^2-2)^2

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

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

Solution steps

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

Expand

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

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

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

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

\int 4 d x = 4 x

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{x ^{6} - 1}{x - 1})

\int_{0}^{1} 3 x^{4} e^{- x} d x

y = - 5 x^{2}, (1, - 5)

20 ln (3 x + 1) - \frac{x}{3}

y = 8 x - x^{2}

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