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

The integral of-sin(x)ln(-2x) is ln(-2x)cos(x)-\Ci(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(x)ln(-2x)

\int - sin (x) ln (- 2 x) d x

ln (- 2 x) cos (x) - Ci (x) + C

Solution steps

\int - sin (x) ln (- 2 x) d x

Take the constant out:

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

= - \int sin (x) ln (- 2 x) d x

Apply Integration By Parts

: - ln (- 2 x) cos (x) - \int - \frac{cos ( x )}{x} d x

= - (- ln (- 2 x) cos (x) - \int - \frac{cos ( x )}{x} d x)

\int - \frac{cos ( x )}{x} d x = - Ci (x)

= - (- ln (- 2 x) cos (x) - (- Ci (x)))

Simplify

= ln (- 2 x) cos (x) - Ci (x)

Add a constant to the solution

= ln (- 2 x) cos (x) - Ci (x) + C

\int 4 x - 8 d x

\int (tan^{2} (2 x) + tan^{4} (2 x)) d x

\int t^{4} e^{t^{5} + 1} d t

\int (x + 7) (x - 5) d x

\int \frac{x e ^{3 x}}{( 3 x + 1 ) ^{2}} d x

What is the integral of-sin(x)ln(-2x) ?
The integral of-sin(x)ln(-2x) is ln(-2x)cos(x)-\Ci(x)+C