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

The integral of tsec^2(2t) is 1/2 ttan(2t)+1/4 ln|cos(2t)|+C

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integral of tsec^2(2t)

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

\frac{1}{2} t tan (2 t) + \frac{1}{4} ln ∣ cos (2 t) ∣ + C

Solution steps

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

Apply Integration By Parts

: \frac{1}{2} t tan (2 t) - \int \frac{1}{2} tan (2 t) d t

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

\int \frac{1}{2} tan (2 t) d t = - \frac{1}{4} ln ∣ cos (2 t) ∣

= \frac{1}{2} t tan (2 t) - (- \frac{1}{4} ln ∣ cos (2 t) ∣)

Simplify

= \frac{1}{2} t tan (2 t) + \frac{1}{4} ln ∣ cos (2 t) ∣

Add a constant to the solution

= \frac{1}{2} t tan (2 t) + \frac{1}{4} ln ∣ cos (2 t) ∣ + C

\int \frac{5 ( x ^{2} + 3 )}{x ( x ^{2} + 5 )} d x

(sin (t))^{2}

\int 2 t \cdot (- cos (2 t)) d t

f (x) = e^{x}, at x = 5

x \to 0 lim (\frac{2}{1 - 2 ^{\frac{1}{x}}})

What is the integral of tsec^2(2t) ?
The integral of tsec^2(2t) is 1/2 ttan(2t)+1/4 ln|cos(2t)|+C