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Calculus Level 5

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

Step 1: 1x(1)dx=1xx(1x2)xdx\displaystyle \int \dfrac{1}{x}(1) dx =\dfrac{1}{x}x-\int \bigg( - \dfrac{1}{x^2} \bigg ) xdx

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

Step 3: 1xdx1xdx=1\displaystyle \int \dfrac{1}{x} dx-\int \dfrac{1}{x} dx=1

Step 4: 0=1 0=1

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

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

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