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Evaluate: inte^xdot(sqrt(1-x^2)sin^(-1)x...

Evaluate: `inte^xdot(sqrt(1-x^2)sin^(-1)x+1)/(sqrt(1-x^2))\ dx`

Text Solution

Verified by Experts

`int e^{x}[frac{sqrt{1-x^{2}} sin ^{-1} x+1}{sqrt{1-x^{2}}}] d x `
` =int e^{x}[sin ^{-1} x+frac{1}{sqrt{1-x^{2}}}] d x`
We know that int `e^{x}[f(x)+f prime(x)] d x=e^{x} cdot f(x)+c`
` =e^{x} cdot sin ^{-1} x+c`
`
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