What is the integral of (cot^2(7x))/(sec(7x)) ?

The integral of (cot^2(7x))/(sec(7x)) is 1/7 cot^2(7x)sin(7x)-2/7 csc(7x)+C

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integral of (cot^2(7x))/(sec(7x))

\int \frac{cot ^{2} ( 7 x )}{sec ( 7 x )} d x

\frac{1}{7} cot^{2} (7 x) sin (7 x) - \frac{2}{7} csc (7 x) + C

Solution steps

\int \frac{cot ^{2} ( 7 x )}{sec ( 7 x )} d x

Apply Integration By Parts

: \frac{1}{7} cot^{2} (7 x) sin (7 x) - \int - 2 csc^{2} (7 x) cot (7 x) sin (7 x) d x

= \frac{1}{7} cot^{2} (7 x) sin (7 x) - \int - 2 csc^{2} (7 x) cot (7 x) sin (7 x) d x

\int - 2 csc^{2} (7 x) cot (7 x) sin (7 x) d x = \frac{2}{7} csc (7 x)

= \frac{1}{7} cot^{2} (7 x) sin (7 x) - \frac{2}{7} csc (7 x)

Add a constant to the solution

= \frac{1}{7} cot^{2} (7 x) sin (7 x) - \frac{2}{7} csc (7 x) + C

\int ln (5 x + 4) d x

\frac{d}{d x} (\frac{1}{sin ( x )} + \frac{1}{cos ( x )})

\frac{d}{d y} (2 4 - y)

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

\frac{d}{d x} (2 sec (x))

What is the integral of (cot^2(7x))/(sec(7x)) ?
The integral of (cot^2(7x))/(sec(7x)) is 1/7 cot^2(7x)sin(7x)-2/7 csc(7x)+C