What is the integral of t^2sec^2(t) ?

The integral of t^2sec^2(t) is t^2tan(t)-i\Li_{2}(-e^{2it})-it^2+2tln(1+cos(2t)+isin(2t))+C

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integral of t^2sec^2(t)

\int t^{2} sec^{2} (t) d t

t^{2} tan (t) - i Li_{2} (- e^{2 i t}) - i t^{2} + 2 t ln (1 + cos (2 t) + i sin (2 t)) + C

Solution steps

\int t^{2} sec^{2} (t) d t

Simplify

t^{2} : tt

= \int tt sec^{2} (t) d t

Apply Integration By Parts

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

\int 2 t tan (t) d t = i Li_{2} (- e^{2 i t}) + i t^{2} - 2 t ln (1 + cos (2 t) + i sin (2 t))

= t^{2} tan (t) - (i Li_{2} (- e^{2 i t}) + i t^{2} - 2 t ln (1 + cos (2 t) + i sin (2 t)))

Simplify

= t^{2} tan (t) - i Li_{2} (- e^{2 i t}) - i t^{2} + 2 t ln (1 + cos (2 t) + i sin (2 t))

Add a constant to the solution

= t^{2} tan (t) - i Li_{2} (- e^{2 i t}) - i t^{2} + 2 t ln (1 + cos (2 t) + i sin (2 t)) + C

What is the integral of t^2sec^2(t) ?
The integral of t^2sec^2(t) is t^2tan(t)-i\Li_{2}(-e^{2it})-it^2+2tln(1+cos(2t)+isin(2t))+C