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

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

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integral of (x^2-pi^2)^2

\int (x^{2} - π^{2})^{2} d x

\frac{x ^{5}}{5} - \frac{2 π ^{2} x ^{3}}{3} + π^{4} x + C

Solution steps

\int (x^{2} - π^{2})^{2} d x

Expand

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

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

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

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

\int π^{4} d x = π^{4} x

= \frac{x ^{5}}{5} - \frac{2 π ^{2} x ^{3}}{3} + π^{4} x

Add a constant to the solution

= \frac{x ^{5}}{5} - \frac{2 π ^{2} x ^{3}}{3} + π^{4} x + C

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