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Question Number 163888 by zakirullah last updated on 11/Jan/22

$$prove\int \frac{1-x^2}{\sqrt{1-x^2}}dx=\int \sqrt{1-x^2}dx$$

Commented by mr W last updated on 12/Jan/22

$$\frac{a^2}{a}=aisobvious.$$

Answered by essojean last updated on 11/Jan/22

$$\int \frac{1-x^2}{\sqrt{1-x^2}}dx=\int (1-x^2)\times {(1-x^2)}^{\frac{-1}{2}}dx$$$$=\int {(1-x^2)}^{1-\frac{1}{2}}dx$$$$=\int {(1-x^2)}^{\frac{1}{2}}dx$$$$=\int \sqrt{1-x^2}dx.....$$$$$$

Commented by zakirullah last updated on 12/Jan/22

$$nicesolutionDearSir$$$$Aboundleofthanks.$$

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