∫ ex(cosec-1x+(-1/x√x2-1)) dx is equal to

Question

∫ ex(cosec-1x+(-1/x√x2-1)) dx is equal to (A)  ex cosec-1 x + C  (B)  ex sin-1 x + C  (C)  ex sec-1 x + C  (D)  ex cos-1 x + C

Tardigrade Admin · Accepted Answer

∫ ex (cosec-1 x+(-1/x√x2-1)) dx =∫ ex cosec-1 x dx-∫ (ex/x√x2-1)dx =[cosec-1x⋅ ex-∫ (-1/x√x2-1) exdx] -∫ (ex/x√x2-1)dx =ex⋅ cosec-1x+∫ (ex/x√x2-1)dx -∫ (ex/√x2-1)⋅ x dx =ex⋅ cosec-1x+c

Q. $\int e^{x} (cose c^{- 1} x + \frac{- 1}{x x ^{2} - 1}) d x$ is equal to

$e^{x} cose c^{- 1} x + C$

$e^{x} s i n^{- 1} x + C$

$e^{x} se c^{- 1} x + C$

$e^{x} co s^{- 1} x + C$

Q. ∫ex(cosec−1x+xx2−1​−1​)dx is equal to

excosec−1x+C

exsin−1x+C

exsec−1x+C

excos−1x+C

∫ex(cosec−1x+xx2−1​−1​)dx =∫excosec−1xdx−∫xx2−1​ex​dx =[cosec−1x⋅ex−∫xx2−1​−1​exdx] −∫xx2−1​ex​dx =ex⋅cosec−1x+∫xx2−1​ex​dx −∫x2−1​ex​⋅xdx =ex⋅cosec−1x+c

Q. $\int e^{x} (cose c^{- 1} x + \frac{- 1}{x x ^{2} - 1}) d x$ is equal to

$e^{x} cose c^{- 1} x + C$

$e^{x} s i n^{- 1} x + C$

$e^{x} se c^{- 1} x + C$

$e^{x} co s^{- 1} x + C$