What is the integral of (cot^2(11x))/(sec(11x)) ?

The integral of (cot^2(11x))/(sec(11x)) is 1/11 cot^2(11x)sin(11x)-2/11 csc(11x)+C

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integral of (cot^2(11x))/(sec(11x))

\int \frac{cot ^{2} ( 11 x )}{sec ( 11 x )} d x

\frac{1}{11} cot^{2} (11 x) sin (11 x) - \frac{2}{11} csc (11 x) + C

Solution steps

\int \frac{cot ^{2} ( 11 x )}{sec ( 11 x )} d x

Apply Integration By Parts

: \frac{1}{11} cot^{2} (11 x) sin (11 x) - \int - 2 csc^{2} (11 x) cot (11 x) sin (11 x) d x

= \frac{1}{11} cot^{2} (11 x) sin (11 x) - \int - 2 csc^{2} (11 x) cot (11 x) sin (11 x) d x

\int - 2 csc^{2} (11 x) cot (11 x) sin (11 x) d x = \frac{2}{11} csc (11 x)

= \frac{1}{11} cot^{2} (11 x) sin (11 x) - \frac{2}{11} csc (11 x)

Add a constant to the solution

= \frac{1}{11} cot^{2} (11 x) sin (11 x) - \frac{2}{11} csc (11 x) + C

2 y^{'} - y^{2} + 4 = 0

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\int \frac{2 x + 1}{x ^{2} + x - 3} d x

\int \frac{ln ( x ^{5} )}{x} d x

\frac{2}{3} t^{2} + 5 e^{- 4 t}

What is the integral of (cot^2(11x))/(sec(11x)) ?
The integral of (cot^2(11x))/(sec(11x)) is 1/11 cot^2(11x)sin(11x)-2/11 csc(11x)+C