What is the integral of (2t^2-3)^2 ?

The integral of (2t^2-3)^2 is (4t^5)/5-4t^3+9t+C

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integral of (2t^2-3)^2

\int (2 t^{2} - 3)^{2} d t

\frac{4 t ^{5}}{5} - 4 t^{3} + 9 t + C

Solution steps

\int (2 t^{2} - 3)^{2} d t

Expand

(2 t^{2} - 3)^{2} : 4 t^{4} - 12 t^{2} + 9

= \int 4 t^{4} - 12 t^{2} + 9 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 4 t^{4} d t - \int 12 t^{2} d t + \int 9 d t

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

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

\int 9 d t = 9 t

= \frac{4 t ^{5}}{5} - 4 t^{3} + 9 t

Add a constant to the solution

= \frac{4 t ^{5}}{5} - 4 t^{3} + 9 t + C

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What is the integral of (2t^2-3)^2 ?
The integral of (2t^2-3)^2 is (4t^5)/5-4t^3+9t+C