What is the integral of-sec(x)sin(x) ?

The integral of-sec(x)sin(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-sec(x)sin(x)

\int - sec (x) sin (x) d x

ln ∣ cos (x) ∣ + C

Solution steps

\int - sec (x) sin (x) d x

Take the constant out:

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

= - \int sec (x) sin (x) d x

Rewrite using trig identities

= - \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) ∣)

Simplify

= ln ∣ cos (x) ∣

Add a constant to the solution

= ln ∣ cos (x) ∣ + C

3 x^{2} (e^{x})^{3}

sin (4 x)

\int \frac{1}{( 1 - 9 x ^{2} ) ^{\frac{3}{2}}} d x

\int \frac{1}{3} x^{5} d x

\int + 9 ln (x^{2} - 1) d x

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