What is the integral of csc(x)sec^2(x) ?

The integral of csc(x)sec^2(x) is sec(x)+ln|tan(x/2)|+C

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integral of csc(x)sec^2(x)

\int csc (x) sec^{2} (x) d x

sec (x) + ln tan (\frac{x}{2}) + C

Solution steps

\int csc (x) sec^{2} (x) d x

Apply Integration By Parts

: sec (x) - \int - cot (x) csc (x) tan (x) d x

= sec (x) - \int - cot (x) csc (x) tan (x) d x

\int - cot (x) csc (x) tan (x) d x = - ln tan (\frac{x}{2})

= sec (x) - (- ln tan (\frac{x}{2}))

Simplify

= sec (x) + ln tan (\frac{x}{2})

Add a constant to the solution

= sec (x) + ln tan (\frac{x}{2}) + C

\int \frac{x ^{2} + 1}{x ^{2} - 5 x + 6} d x

\frac{\partial}{\partial x} (5 e^{2 x})

y = \frac{x ^{4}}{4} + \frac{2}{9} x^{3} - x^{2} + 9 x - 5

\frac{( 2 x )}{1 + x ^{4}}

7 - 4 x

What is the integral of csc(x)sec^2(x) ?
The integral of csc(x)sec^2(x) is sec(x)+ln|tan(x/2)|+C