Integral of -x*sin(4)^3

The calculator will find the integral/antiderivative of $$$- x \sin^{3}{\left(4 \right)}$$$, with steps shown.

Related calculator: Definite and Improper Integral Calculator

Your Input

Find $$$\int \left(- x \sin^{3}{\left(4 \right)}\right)\, dx$$$.

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 $$$c=- \sin^{3}{\left(4 \right)}$$$ and $$$f{\left(x \right)} = x$$$:

$${\color{red}{\int{\left(- x \sin^{3}{\left(4 \right)}\right)d x}}} = {\color{red}{\left(- \sin^{3}{\left(4 \right)} \int{x d x}\right)}}$$

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

$$- \sin^{3}{\left(4 \right)} {\color{red}{\int{x d x}}}=- \sin^{3}{\left(4 \right)} {\color{red}{\frac{x^{1 + 1}}{1 + 1}}}=- \sin^{3}{\left(4 \right)} {\color{red}{\left(\frac{x^{2}}{2}\right)}}$$

Therefore,

$$\int{\left(- x \sin^{3}{\left(4 \right)}\right)d x} = - \frac{x^{2} \sin^{3}{\left(4 \right)}}{2}$$

Add the constant of integration:

$$\int{\left(- x \sin^{3}{\left(4 \right)}\right)d x} = - \frac{x^{2} \sin^{3}{\left(4 \right)}}{2}+C$$

Answer

$$$\int \left(- x \sin^{3}{\left(4 \right)}\right)\, dx = - \frac{x^{2} \sin^{3}{\left(4 \right)}}{2} + C$$$A

Please try a new game Rotatly

Integral of $$$- x \sin^{3}{\left(4 \right)}$$$

Your Input

Solution

Answer