What is the integral of (cos(t))/(sin^2(t)) ?

The integral of (cos(t))/(sin^2(t)) is -csc(t)+C

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integral of (cos(t))/(sin^2(t))

\int \frac{cos ( t )}{sin ^{2} ( t )} d t

- csc (t) + C

Solution steps

\int \frac{cos ( t )}{sin ^{2} ( t )} d t

Apply u-substitution

: \int \frac{1}{u ^{2}} d u

= \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{u}

Substitute back

u = sin (t)

= - \frac{1}{sin ( t )}

Use the basic trigonometric identity:

\frac{1}{sin ( x )} = csc (x)

= - csc (t)

Add a constant to the solution

= - csc (t) + C

\frac{\partial}{\partial y} (3 y cos (π x) + 2 x z)

y^{^{'}} = \frac{3}{x} (y^{2} + y), y (4) = 2

\int \frac{1}{v} d v

5 \cdot e^{- 3 x} \cdot sin (5 x) \cdot x

x \to 3 lim (5 - x)

What is the integral of (cos(t))/(sin^2(t)) ?
The integral of (cos(t))/(sin^2(t)) is -csc(t)+C