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`int(dx)/((25-19x^(2)))` का मान ज्ञात कीजिये |

Answer» माना `I = int (dx)/(sqrt(25-16x)) = (1)/(4) int(dx)/(1+((3x)/(2))^(2))`
माना `(4x )/(5)=sin theta" " rArr dx = (5)/(4) cos theta d theta`
`therefore theta = sin^(-1)((4x)/(5))`
`therefore I = (1)/(5) xx(5)/(4) int (cos theta d theta)/(sqrt(1-sin ^(2) theta)) = (1)/(4) int (cos theta d theta)/(cos theta)`
` = (1)/(4) int d theta = (1)/(4) theta = (1)/(4) sin ^(-1)((4x)/(5))`


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