Q.1 (A) (ii) \(\int\left(x+\frac{1}{x}\right)^3dx=\)
A. \(\frac{1}{4}\left(x+\frac{1}{x}\right)^4+c\)
B. \(\frac{x^4}{4}+\frac{3x^2}{2}+3\log x-\frac{1}{2x^2}+c\)
C. \(\frac{x^4}{4}+\frac{3x^2}{2}+3\log x+\frac{1}{x^2}+c\)
D. \(\left(x-x^{-1}\right)^3+c\)
Best answer
Answer: B. \(\frac{x^4}{4}+\frac{3x^2}{2}+3\log x-\frac{1}{2x^2}+c\)
Answer: (b) \(\frac{x^4}{4}+\frac{3x^2}{2}+3\log x-\frac{1}{2x^2}+c\)
\(\left(x+\frac{1}{x}\right)^3=x^3+3x+\frac{3}{x}+x^{-3}\).
\(\int\left(x^3+3x+\frac{3}{x}+x^{-3}\right)dx=\frac{x^4}{4}+\frac{3x^2}{2}+3\log x+\frac{x^{-2}}{-2}+c=\frac{x^4}{4}+\frac{3x^2}{2}+3\log x-\frac{1}{2x^2}+c\)
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