1) 1 2) – 1 3) 0 4) 2 Solution: (2) – 1 \(\begin{array}{l}\begin{array}{l} \frac{d}{d x}\left[\operatorname{atan}^{-1} x+b \ln \left(\frac{x-1}{x+1}\right)\right]=\frac{1}{x^{4}-1} \\... View Article

If (d / dx) (f (x)) = 1 / (1 + x²), then (d / dx) (f (x³)) =

1) 3x / (1 + x3) 2) 3x2 / (1 + x6) 3) (- 6x5) / (1 + x6)2 4)... View Article

∫(x + 1) (x + 2)⁷ (x + 3) dx =

1) [(x + 2)10 / 10] – [(x + 2)8 / 8] + c 2) [(x + 1)2 / 2]... View Article

∫cosec (x – a) cosec x dx =

1) (1 / sin a) log |sin (x – a) / sin x| + C 2) (- 1 / sin... View Article

∫(x⁴ + x² + 1) / (x² – x + 1) dx =

1) (x3 / 3) – (x2 / 2) + x + C 2) (x3 / 3) + (x2 / 2)... View Article

∫[sin (log x) + cos (log x)] dx =

1) x cos (log x) + C 2) cos (log x) + C 3) x sin (log x) + C... View Article

∫[d (cos θ) / (√1 – cos² θ)] =

1) cos-1 θ + C 2) θ + C 3) sin-1 θ + C 4) sin-1 (cos θ) + C... View Article

If f [(3x – 4) / (3x + 4)] = x + 2, then ∫f (x) dx =

1) ex+2 log |(3x – 4) / (3x + 4)| + c 2) (- 8 / 3) log |1 –... View Article

∫1 / [sin (x – a) sin (x – b)] dx =

1) 1 / [sin (b – a)] log |[(sin (x + b)) / (sin (x + a))| + c 2)... View Article

The value of ∫(sin x + cos x) / [√(1 + sin 2x)] dx is

1) √(1 + cos 2x) + c 2) √x – c 3) x + c 4) √(x + 2x) +... View Article

∫(sin⁸ x – cos⁸ x) / (1 – 2 sin² x cos² x) dx =

1) (- 1 / 2) sin 2x + c 2) (1 / 2) sin 2x + c 3) (1 /... View Article

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