Integral of $$$x^{\frac{43}{2}}$$$

Find $$$\int x^{\frac{43}{2}}\, dx$$$.

Apply the power rule $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=\frac{43}{2}$$$:

$${\color{red}{\int{x^{\frac{43}{2}} d x}}}={\color{red}{\frac{x^{1 + \frac{43}{2}}}{1 + \frac{43}{2}}}}={\color{red}{\left(\frac{2 x^{\frac{45}{2}}}{45}\right)}}$$

Therefore,

$$\int{x^{\frac{43}{2}} d x} = \frac{2 x^{\frac{45}{2}}}{45}$$

Add the constant of integration:

$$\int{x^{\frac{43}{2}} d x} = \frac{2 x^{\frac{45}{2}}}{45}+C$$

$$$\int x^{\frac{43}{2}}\, dx = \frac{2 x^{\frac{45}{2}}}{45} + C$$$A