What is the integral of cot(x)sqrt(1-cos(2x)) ?

The integral of cot(x)sqrt(1-cos(2x)) is sqrt(2)sin(x)+C

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integral of cot(x)sqrt(1-cos(2x))

\int cot (x) 1 - cos (2 x) d x

2 sin (x) + C

Solution steps

\int cot (x) 1 - cos (2 x) d x

1 - cos (2 x) = 2 sin (x)

= \int 2 cot (x) sin (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int cot (x) sin (x) d x

Express with sin, cos

= 2 \cdot \int cos (x) d x

Use the common integral:

\int cos (x) d x = sin (x)

= 2 sin (x)

Add a constant to the solution

= 2 sin (x) + C

\int \frac{x ^{2} + 4 x + 1}{( x ^{2} - 1 ) ( x + 3 )} d x

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

\int \frac{tan ^{8} ( x )}{sec ^{9} ( x )} d x

\int (tan^{3} (3 x) sec^{4} (3 x)) d x

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

What is the integral of cot(x)sqrt(1-cos(2x)) ?
The integral of cot(x)sqrt(1-cos(2x)) is sqrt(2)sin(x)+C