What is the integral of 3tan(5x) ?

The integral of 3tan(5x) is -3/5 ln|cos(5x)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3tan(5x)

\int 3 tan (5 x) d x

- \frac{3}{5} ln ∣ cos (5 x) ∣ + C

Solution steps

\int 3 tan (5 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 (5 x) d x

Rewrite using trig identities

= 3 \cdot \int \frac{sin ( 5 x )}{cos ( 5 x )} d x

Apply u-substitution

: \int - \frac{1}{5 u} d u

= 3 \cdot \int - \frac{1}{5 u} d u

Take the constant out:

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

= 3 (- \frac{1}{5} \cdot \int \frac{1}{u} d u)

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 (- \frac{1}{5} ln ∣ u ∣)

Substitute back

u = cos (5 x)

= 3 (- \frac{1}{5} ln ∣ cos (5 x) ∣)

Simplify

3 (- \frac{1}{5} ln ∣ cos (5 x) ∣) : - \frac{3}{5} ln ∣ cos (5 x) ∣

= - \frac{3}{5} ln ∣ cos (5 x) ∣

Add a constant to the solution

= - \frac{3}{5} ln ∣ cos (5 x) ∣ + C

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

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

\int \frac{4 x + 2}{x ^{2} + x} d x

\int \frac{1}{x ^{5} x ^{2} - 9} d x

\int n a^{c o s (b t)} sin (b t) d t

What is the integral of 3tan(5x) ?
The integral of 3tan(5x) is -3/5 ln|cos(5x)|+C