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प्रश्न
`int{sqrtx(ax^2+bx+c)}dx`
योग
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उत्तर
`int{sqrtx(ax^2+bx+c)}dx`
Treat `sqrtx = x^(1/2) "and integrate term-by-term (power rule" intx^ndx = (x^(n+1))/(n+1)`
`intsqrtx(ax^2+bx+c)dx=a intx^(5/2)dx +b intx^(3/2)dx+c intx^(1/2)dx`
`= a . 2/7 x^(7/2)+ b . 2/5x^(5/2) + c . 2/3 x^(3/2) + C`
`=(2a)/7 x^(7/2) + (2b)/5 x^(5/2) + (2c)/3 x^(3/2) + C`
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