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

\int \frac{tan ^{2} ( x ) + sec ^{2} ( x )}{tan ( x )} d x

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

f (x) = 12 x^{3} - \frac{1}{x}

x^{2} + 2 x + 2

(126 - 0.5 x) x - 50 x - 31.75

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