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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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