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Calculus Level 5

Consider the integral, $I=\displaystyle \int \dfrac{1}{x} dx$

Step 1: $\displaystyle \int \dfrac{1}{x}(1) dx =\dfrac{1}{x}x-\int \bigg( - \dfrac{1}{x^2} \bigg ) xdx$

Step 2: $\displaystyle \int \dfrac{1}{x} dx=1+\int \dfrac{1}{x} dx$

Step 3: $\displaystyle \int \dfrac{1}{x} dx-\int \dfrac{1}{x} dx=1$

Step 4: $0=1$

Which of the above step/s is/are wrong?

If steps a,b,c... are wrong, enter your answer as $a \times b \times c \times ..$

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