What is the integral of xcos(x)+cos(x)-1 ?

The integral of xcos(x)+cos(x)-1 is xsin(x)+cos(x)+sin(x)-x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of xcos(x)+cos(x)-1

\int x cos (x) + cos (x) - 1 d x

x sin (x) + cos (x) + sin (x) - x + C

Solution steps

\int x cos (x) + cos (x) - 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x cos (x) d x + \int cos (x) d x - \int 1 d x

\int x cos (x) d x = x sin (x) + cos (x)

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

\int 1 d x = x

= x sin (x) + cos (x) + sin (x) - x

Add a constant to the solution

= x sin (x) + cos (x) + sin (x) - x + C

\int cos^{2} (x) - sin^{2} (x) d x

(t - 3)^{4}

\frac{d}{d x} (e^{2 x} + 5)

(2 x y^{2} - 7) d x + (2 x^{2} y + 5) d y = 0

\frac{d}{d x} (8 e^{x} + \frac{4}{3 x})

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