What is the integral of cot(11t)sqrt(1-sin^2(11t)) ?

The integral of cot(11t)sqrt(1-sin^2(11t)) is 1/11 cot(11t)sin(11t)+1/11 ln|tan((11t)/2)|+C

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integral of cot(11t)sqrt(1-sin^2(11t))

\int cot (11 t) 1 - sin^{2} (11 t) d t

\frac{1}{11} cot (11 t) sin (11 t) + \frac{1}{11} ln tan (\frac{11 t}{2}) + C

Solution steps

\int cot (11 t) 1 - sin^{2} (11 t) d t

Apply Integration By Parts

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

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

\int - csc^{2} (11 t) sin (11 t) d t = - \frac{1}{11} ln tan (\frac{11 t}{2})

= \frac{1}{11} cot (11 t) sin (11 t) - (- \frac{1}{11} ln tan (\frac{11 t}{2}))

Simplify

= \frac{1}{11} cot (11 t) sin (11 t) + \frac{1}{11} ln tan (\frac{11 t}{2})

Add a constant to the solution

= \frac{1}{11} cot (11 t) sin (11 t) + \frac{1}{11} ln tan (\frac{11 t}{2}) + C

f (x) = a x^{2} + b x

\int \frac{2}{x ^{0.85}} d x

\frac{\partial}{\partial x} (2 x y + x f (x, y) (\frac{y}{x}))

\frac{\partial}{\partial y} (3 + 2 x y)

5 x, 3 x^{2}

What is the integral of cot(11t)sqrt(1-sin^2(11t)) ?
The integral of cot(11t)sqrt(1-sin^2(11t)) is 1/11 cot(11t)sin(11t)+1/11 ln|tan((11t)/2)|+C