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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\int \frac{1}{2 + 2 cos ( x )} d x

\frac{d y}{d x} = x e^{x^{2} - y}

\int x^{3} \cdot e^{x^{2}} d x

\int \frac{8}{x} + 8 x d x

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