What is the integral of x*tan(x^2) ?

The integral of x*tan(x^2) is -1/2 ln|cos(x^2)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x*tan(x^2)

\int x \cdot tan (x^{2}) d x

- \frac{1}{2} ln cos (x^{2}) + C

Solution steps

\int x tan (x^{2}) d x

Apply u-substitution

: \int \frac{tan ( u )}{2} d u

= \int \frac{tan ( u )}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int tan (u) d u

Rewrite using trig identities

= \frac{1}{2} \cdot \int \frac{sin ( u )}{cos ( u )} d u

Apply u-substitution

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

= \frac{1}{2} \cdot \int - \frac{1}{v} d v

Take the constant out:

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

= \frac{1}{2} (- \int \frac{1}{v} d v)

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= \frac{1}{2} (- ln ∣ v ∣)

Substitute back

= \frac{1}{2} (- ln cos (x^{2}))

Simplify

= - \frac{1}{2} ln cos (x^{2})

Add a constant to the solution

= - \frac{1}{2} ln cos (x^{2}) + C

3 \cdot e^{- s}

x (x^{2} - 4 x + 5)^{4}, at x = 2

x \to 4 + lim (\frac{x + 2}{x - 4})

\int_{3}^{5} x \cdot \frac{x}{8} d x

\frac{8}{sin ( x ) + cos ( x )}

What is the integral of x*tan(x^2) ?
The integral of x*tan(x^2) is -1/2 ln|cos(x^2)|+C