What is the integral of (tan(3x))/(cos(3x)) ?

The integral of (tan(3x))/(cos(3x)) is 1/3 sec(3x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (tan(3x))/(cos(3x))

\int \frac{tan ( 3 x )}{cos ( 3 x )} d x

\frac{1}{3} sec (3 x) + C

Solution steps

\int \frac{tan ( 3 x )}{cos ( 3 x )} d x

Apply u-substitution

: \int \frac{tan ( u )}{3 cos ( u )} d u

= \int \frac{tan ( u )}{3 cos ( u )} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int \frac{tan ( u )}{cos ( u )} d u

Rewrite using trig identities

= \frac{1}{3} \cdot \int tan (u) sec (u) d u

Apply u-substitution

: \int 1 d v

= \frac{1}{3} \cdot \int 1 d v

Integral of a constant:

\int a d x = a x

= \frac{1}{3} \cdot 1 \cdot v

Substitute back

= \frac{1}{3} \cdot 1 \cdot sec (3 x)

Simplify

= \frac{1}{3} sec (3 x)

Add a constant to the solution

= \frac{1}{3} sec (3 x) + C

5 y^{^{''}} + y^{^{'}} = - 10 x, y (0) = 0, y^{^{'}} (0) = - 15

f (x) = \frac{2 x + 1}{x + 2}, (1, 1)

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

\frac{d y}{d x} = y^{2} x^{3}

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

What is the integral of (tan(3x))/(cos(3x)) ?
The integral of (tan(3x))/(cos(3x)) is 1/3 sec(3x)+C