What is the integral of-3tan(x) ?

The integral of-3tan(x) is 3ln|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-3tan(x)

\int - 3 tan (x) d x

3 ln ∣ cos (x) ∣ + C

Solution steps

\int - 3 tan (x) d x

Take the constant out:

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

= - 3 \cdot \int tan (x) d x

Rewrite using trig identities

= - 3 \cdot \int \frac{sin ( x )}{cos ( x )} d x

Apply u-substitution

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

= - 3 \cdot \int - \frac{1}{u} d u

Take the constant out:

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

= - 3 (- \int \frac{1}{u} d u)

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - 3 (- ln ∣ u ∣)

Substitute back

u = cos (x)

= - 3 (- ln ∣ cos (x) ∣)

Simplify

= 3 ln ∣ cos (x) ∣

Add a constant to the solution

= 3 ln ∣ cos (x) ∣ + C

y^{^{'}} = \frac{5 x ^{6} e ^{\frac{y}{x}} + x ^{4} y ^{2}}{x ^{5} y}

(e^{x} + 1)^{7}

8 y^{^{'}} + t y = 7

\frac{1}{x - 1}