Integral of 13*x^2*cos(1)/2

The calculator will find the integral/antiderivative of $$$\frac{13 x^{2} \cos{\left(1 \right)}}{2}$$$, with steps shown.

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Find $$$\int \frac{13 x^{2} \cos{\left(1 \right)}}{2}\, dx$$$.

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 $$$c=\frac{13 \cos{\left(1 \right)}}{2}$$$ and $$$f{\left(x \right)} = x^{2}$$$:

$${\color{red}{\int{\frac{13 x^{2} \cos{\left(1 \right)}}{2} d x}}} = {\color{red}{\left(\frac{13 \cos{\left(1 \right)} \int{x^{2} d x}}{2}\right)}}$$

Apply the power rule $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=2$$$:

$$\frac{13 \cos{\left(1 \right)} {\color{red}{\int{x^{2} d x}}}}{2}=\frac{13 \cos{\left(1 \right)} {\color{red}{\frac{x^{1 + 2}}{1 + 2}}}}{2}=\frac{13 \cos{\left(1 \right)} {\color{red}{\left(\frac{x^{3}}{3}\right)}}}{2}$$

Therefore,

$$\int{\frac{13 x^{2} \cos{\left(1 \right)}}{2} d x} = \frac{13 x^{3} \cos{\left(1 \right)}}{6}$$

Add the constant of integration:

$$\int{\frac{13 x^{2} \cos{\left(1 \right)}}{2} d x} = \frac{13 x^{3} \cos{\left(1 \right)}}{6}+C$$

Answer

$$$\int \frac{13 x^{2} \cos{\left(1 \right)}}{2}\, dx = \frac{13 x^{3} \cos{\left(1 \right)}}{6} + C$$$A

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Integral of $$$\frac{13 x^{2} \cos{\left(1 \right)}}{2}$$$

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