What is the integral of csc(z+pi/4)cot(z+pi/4) ?

The integral of csc(z+pi/4)cot(z+pi/4) is -csc(z+pi/4)+C

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integral of csc(z+pi/4)cot(z+pi/4)

\int csc (z + \frac{π}{4}) cot (z + \frac{π}{4}) d z

- csc (z + \frac{π}{4}) + C

Solution steps

\int csc (z + \frac{π}{4}) cot (z + \frac{π}{4}) d z

Apply u-substitution

: \int csc (u) cot (u) d u

= \int csc (u) cot (u) d u

Apply u-substitution

: \int - 1 d v

= \int - 1 d v

Integral of a constant:

\int a d x = a x

= (- 1) v

Substitute back

= (- 1) csc (z + \frac{π}{4})

Simplify

= - csc (z + \frac{π}{4})

Add a constant to the solution

= - csc (z + \frac{π}{4}) + C

\frac{d}{d x} (0.02 x^{3} - 0.07 x^{2} + 8 x)

\frac{d}{d x} (cos^{4} (2 x))

\int \frac{x}{x ^{2} - 6} d x

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

\frac{d}{d x} (\frac{e ^{2 x}}{2 x})

What is the integral of csc(z+pi/4)cot(z+pi/4) ?
The integral of csc(z+pi/4)cot(z+pi/4) is -csc(z+pi/4)+C