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

\frac{\partial}{\partial y} (\frac{y}{( x + y ) ^{2}})

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

f (t) = t^{\frac{5}{3}} e^{t}

\int_{0}^{\infty} e^{- x} cos (x) d x

\frac{\partial}{\partial x} (e^{- 2 t} cos (π 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