What is the integral of (sin(y))/(cos(y)) ?

The integral of (sin(y))/(cos(y)) is -ln|cos(y)|+C

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integral of (sin(y))/(cos(y))

\int \frac{sin ( y )}{cos ( y )} d y

- ln ∣ cos (y) ∣ + C

Solution steps

\int \frac{sin ( y )}{cos ( y )} d y

Apply u-substitution

: \int - \frac{1}{u} d u

= \int - \frac{1}{u} d u

Take the constant out:

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

= - \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - ln ∣ u ∣

Substitute back

u = cos (y)

= - ln ∣ cos (y) ∣

Add a constant to the solution

= - ln ∣ cos (y) ∣ + C

\frac{\partial}{\partial y} (- e^{- x} sin (y))

\frac{\partial}{\partial y} (4 x^{2} + 4 x y - 3 y^{2} + 4 y - 1)

x \to 1 lim (x - 1)

\int sec^{2} (x) + sec (2 x) tan (2 x) d x

p (θ) = 7 θ

What is the integral of (sin(y))/(cos(y)) ?
The integral of (sin(y))/(cos(y)) is -ln|cos(y)|+C