What is the integral of xcot(x^2)sin(ln(sin(x^2))) ?

The integral of xcot(x^2)sin(ln(sin(x^2))) is -1/2 cos(ln(sin(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 xcot(x^2)sin(ln(sin(x^2)))

\int x cot (x^{2}) sin (ln (sin (x^{2}))) d x

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

Solution steps

\int x cot (x^{2}) sin (ln (sin (x^{2}))) d x

Apply u-substitution

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

= \int \frac{sin ( 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 sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= \frac{1}{2} (- cos (u))

Substitute back

u = ln (sin (x^{2}))

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

Simplify

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

Add a constant to the solution

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

\int \frac{1}{( x - 4 ) ( 8 - x )} d x

\int - x^{- 3} + x - 1 d x

\int - 1536 (1 + 8 x)^{- 3} d x

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

\int x 6 x^{2} + 3 d x

What is the integral of xcot(x^2)sin(ln(sin(x^2))) ?
The integral of xcot(x^2)sin(ln(sin(x^2))) is -1/2 cos(ln(sin(x^2)))+C