Integral of x*cos(2)

The calculator will find the integral/antiderivative of

x \cos{\left(2 \right)}

, with steps shown.

Related calculator: Definite and Improper Integral Calculator

Your Input

Find $\int x \cos{\left(2 \right)}\, dx$ .

The trigonometric functions expect the argument in radians. To enter the argument in degrees, multiply it by pi/180, e.g. write 45° as 45*pi/180, or use the appropriate function adding 'd', e.g. write sin(45°) as sind(45).

Solution

Apply the constant multiple rule $\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$ with $c=\cos{\left(2 \right)}$ and $f{\left(x \right)} = x$ :

${\color{red}{\int{x \cos{\left(2 \right)} d x}}} = {\color{red}{\cos{\left(2 \right)} \int{x d x}}}$

Apply the power rule $\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$ $\left(n \neq -1 \right)$ with $n=1$ :

$\cos{\left(2 \right)} {\color{red}{\int{x d x}}}=\cos{\left(2 \right)} {\color{red}{\frac{x^{1 + 1}}{1 + 1}}}=\cos{\left(2 \right)} {\color{red}{\left(\frac{x^{2}}{2}\right)}}$

Therefore,

$\int{x \cos{\left(2 \right)} d x} = \frac{x^{2} \cos{\left(2 \right)}}{2}$

Add the constant of integration:

$\int{x \cos{\left(2 \right)} d x} = \frac{x^{2} \cos{\left(2 \right)}}{2}+C$

Answer

$\int x \cos{\left(2 \right)}\, dx = \frac{x^{2} \cos{\left(2 \right)}}{2} + C$ A

Integral of xcos⁡(2)x \cos{\left(2 \right)}xcos(2)

Your Input

Solution

Answer

Integral of $x \cos{\left(2 \right)}$