定積分・広義積分計算機
定積分と広義積分を手順を追って計算する
この計算機は、定積分（すなわち上下限のある積分）を、広義積分も含めて、解法手順を示しながら計算を試みます。
Solution
Your input: calculate $$$\int_{1}^{9}\left( \frac{- x^{\frac{3}{2}} + 4 x^{5} - 3}{x^{2}} \right)dx$$$
First, calculate the corresponding indefinite integral: $$$\int{\frac{- x^{\frac{3}{2}} + 4 x^{5} - 3}{x^{2}} d x}=\frac{- 2 x^{\frac{3}{2}} + x^{5} + 3}{x}$$$ (for steps, see indefinite integral calculator)
According to the Fundamental Theorem of Calculus, $$$\int_a^b F(x) dx=f(b)-f(a)$$$, so just evaluate the integral at the endpoints, and that's the answer.
$$$\left(\frac{- 2 x^{\frac{3}{2}} + x^{5} + 3}{x}\right)|_{\left(x=9\right)}=\frac{19666}{3}$$$
$$$\left(\frac{- 2 x^{\frac{3}{2}} + x^{5} + 3}{x}\right)|_{\left(x=1\right)}=2$$$
$$$\int_{1}^{9}\left( \frac{- x^{\frac{3}{2}} + 4 x^{5} - 3}{x^{2}} \right)dx=\left(\frac{- 2 x^{\frac{3}{2}} + x^{5} + 3}{x}\right)|_{\left(x=9\right)}-\left(\frac{- 2 x^{\frac{3}{2}} + x^{5} + 3}{x}\right)|_{\left(x=1\right)}=\frac{19660}{3}$$$
Answer: $$$\int_{1}^{9}\left( \frac{- x^{\frac{3}{2}} + 4 x^{5} - 3}{x^{2}} \right)dx=\frac{19660}{3}\approx 6553.33333333333$$$