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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 $$$\int_{0}^{2}\left( \ln{\left(x - 5 \right)} \right)dx$$$
First, calculate the corresponding indefinite integral: $$$\int{\ln{\left(x - 5 \right)} d x}=\left(x - 5\right) \left(\ln{\left(x - 5 \right)} - 1\right)$$$ (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.
$$$\left(\left(x - 5\right) \left(\ln{\left(x - 5 \right)} - 1\right)\right)|_{\left(x=2\right)}=- 3 \ln{\left(3 \right)} + 3 - 3 i \pi$$$
$$$\left(\left(x - 5\right) \left(\ln{\left(x - 5 \right)} - 1\right)\right)|_{\left(x=0\right)}=- 5 \ln{\left(5 \right)} + 5 - 5 i \pi$$$
$$$\int_{0}^{2}\left( \ln{\left(x - 5 \right)} \right)dx=\left(\left(x - 5\right) \left(\ln{\left(x - 5 \right)} - 1\right)\right)|_{\left(x=2\right)}-\left(\left(x - 5\right) \left(\ln{\left(x - 5 \right)} - 1\right)\right)|_{\left(x=0\right)}=- 3 \ln{\left(3 \right)} - 2 + 5 \ln{\left(5 \right)} + 2 i \pi$$$
Answer: $$$\int_{0}^{2}\left( \ln{\left(x - 5 \right)} \right)dx=- 3 \ln{\left(3 \right)} - 2 + 5 \ln{\left(5 \right)} + 2 i \pi\approx 2.75135269616617 + 6.28318530717959 i$$$