What is the integral of-1/(csc(y)) ?

The integral of-1/(csc(y)) is cos(y)+C

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integral of-1/(csc(y))

\int - \frac{1}{csc ( y )} d y

cos (y) + C

Solution steps

\int - \frac{1}{csc ( y )} d y

Take the constant out:

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

= - \int \frac{1}{csc ( y )} d y

Rewrite using trig identities

= - \int sin (y) d y

Use the common integral:

\int sin (y) d y = - cos (y)

= - (- cos (y))

Simplify

= cos (y)

Add a constant to the solution

= cos (y) + C

\frac{d}{d x} (cos^{2} (ln (x + 1)) - e^{x^{2}})

y = 5 x - 1

\int_{\frac{π}{2}}^{π} 2 cot (\frac{x}{3}) d x

x \to 1 lim (\frac{x + 1}{x ^{3} + 1})