"Find the following integral. ∫(2t2−1)2dt" was answered by our community

Lennie Carroll

Answered question

2021-10-14

Find the following integral.

\int {(2 t^{2} - 1)}^{2} d t

Elberte

Skilled2021-10-15Added 95 answers

\int {(2 t^{2} - 1)}^{2} d t

= \int (2 t^{2} - 1) (2 t^{2} - 1) d t

= \int (4 t^{4} - 2 t^{2} - 2 t^{2} + 1) d t

= \int (4 t^{4} - 4 t^{2} + 1) d t

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

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

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