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

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

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integral of ((sin(x))/(cos(x)))

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

- ln ∣ cos (x) ∣ + C

Solution steps

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

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 (x)

= - ln ∣ cos (x) ∣

Add a constant to the solution

= - ln ∣ cos (x) ∣ + C

\frac{d}{d x} (\frac{y - x ^{2} + 2}{x - y})

y^{^{'}} = \frac{y ^{2} + 2}{x y - 4 y}

\frac{\partial}{\partial x} (x y e^{4 y})

y = x^{2} + 6 x - 5, at x = 2

\int x^{9} e^{x^{10}} d x

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