Evaluate the Integral $$\int x \sin ^ { - 1 } x d x$$

question 238

Multiple Choice

Evaluate the integral.
- $$\int x \sin ^ { - 1 } x d x$$

• A) \(\frac { x ^ { 2 } } { 2 } \sin ^ { - 1 } x - \frac { 1 } { 4 } x \sin ^ { - 1 } x - \frac { 1 } { 4 } \sqrt { 1 - x ^ { 2 } } + C\)
• B) \(\frac { x ^ { 2 } } { 2 } \sin ^ { - 1 } x + \frac { 1 } { 2 } \sin ^ { - 1 } x - \frac { 1 } { 2 } x \sqrt { 1 - x ^ { 2 } } + C\)
• C) \(\frac { x ^ { 2 } } { 2 } \sin ^ { - 1 } x - \frac { 1 } { 4 } \sin ^ { - 1 } x + \frac { 1 } { 4 } x \sqrt { 1 - x ^ { 2 } } + C\)
• D) \(\frac { x ^ { 2 } } { 2 } \sin ^ { - 1 } x - \frac { 1 } { 4 } \cos ^ { - 1 } x + \frac { 1 } { 4 } \sqrt { 1 - x ^ { 2 } } + C\)

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