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Consider the integral, I=∫1xdx I=\displaystyle \int \dfrac{1}{x} dxI=∫x1dx
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 ∫x1(1)dx=x1x−∫(−x21)xdx
Step 2: ∫1xdx=1+∫1xdx\displaystyle \int \dfrac{1}{x} dx=1+\int \dfrac{1}{x} dx ∫x1dx=1+∫x1dx
Step 3: ∫1xdx−∫1xdx=1\displaystyle \int \dfrac{1}{x} dx-\int \dfrac{1}{x} dx=1 ∫x1dx−∫x1dx=1
Step 4: 0=1 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 .. a×b×c×..
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