정적분 및 가적분 계산기

이 계산기는 단계별 풀이를 보여 주면서 상한과 하한이 있는 정적분(진정적분 포함)을 계산하려고 시도합니다.

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Integrate with respect to:

Enter a lower limit:

If you need `-oo`, type -inf.

Enter an upper limit:

If you need `oo`, type inf.

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Solution

Your input: calculate $$$\int_{0}^{x}\left( \frac{1}{x} \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{\frac{1}{x} d x}=\ln{\left(\left|{x}\right| \right)}$$$ (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.

$$$\left(\ln{\left(\left|{x}\right| \right)}\right)|_{\left(x=x\right)}=\ln{\left(\left|{x}\right| \right)}$$$

$$$\left(\ln{\left(\left|{x}\right| \right)}\right)|_{\left(x=0\right)}=-\infty$$$

$$$\int_{0}^{x}\left( \frac{1}{x} \right)dx=\left(\ln{\left(\left|{x}\right| \right)}\right)|_{\left(x=x\right)}-\left(\ln{\left(\left|{x}\right| \right)}\right)|_{\left(x=0\right)}=\ln{\left(\left|{x}\right| \right)} + \infty$$$

Answer: $$$\int_{0}^{x}\left( \frac{1}{x} \right)dx=\ln{\left(\left|{x}\right| \right)} + \infty$$$

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정적분 및 가적분 계산기

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Solution