What is the integral of sin(ln(x)) ?

The integral of sin(ln(x)) is 1/2 xsin(ln(x))-1/2 xcos(ln(x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(ln(x))

\int sin (ln (x)) d x

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

Solution steps

\int sin (ln (x)) d x

Apply Integration By Parts

: x sin (ln (x)) - \int cos (ln (x)) d x

= x sin (ln (x)) - \int cos (ln (x)) d x

\int cos (ln (x)) d x = \frac{1}{2} x sin (ln (x)) + \frac{1}{2} x cos (ln (x))

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

Simplify

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

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

Add a constant to the solution

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

\int 0.5 x d x

y^{^{''}} + 9 y = cos (3 x)

x \to - 8 lim (x (8))

\frac{d}{d x} (\frac{1}{x} - ln (x))

\frac{\partial}{\partial z} (tan (3 + 2 x^{2} y^{3} z^{2}))

What is the integral of sin(ln(x)) ?
The integral of sin(ln(x)) is 1/2 xsin(ln(x))-1/2 xcos(ln(x))+C