What is the integral of (t^2-6)^2 ?

The integral of (t^2-6)^2 is (t^5)/5-4t^3+36t+C

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integral of (t^2-6)^2

\int (t^{2} - 6)^{2} d t

\frac{t ^{5}}{5} - 4 t^{3} + 36 t + C

Solution steps

\int (t^{2} - 6)^{2} d t

Expand

(t^{2} - 6)^{2} : t^{4} - 12 t^{2} + 36

= \int t^{4} - 12 t^{2} + 36 d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int t^{4} d t - \int 12 t^{2} d t + \int 36 d t

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

\int 12 t^{2} d t = 4 t^{3}

\int 36 d t = 36 t

= \frac{t ^{5}}{5} - 4 t^{3} + 36 t

Add a constant to the solution

= \frac{t ^{5}}{5} - 4 t^{3} + 36 t + C

What is the integral of (t^2-6)^2 ?
The integral of (t^2-6)^2 is (t^5)/5-4t^3+36t+C