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प्रश्न
Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`
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उत्तर
We are asked to evaluate:
`int(x-2)/sqrt(x+5) dx`
u = x + 5
`(du)/dx = 1 => du=dx`
x = u − 5
`int ((u-5)-2)/sqrtu du = int (u-7)/sqrtu du`
`= int (u/sqrtu-7/sqrtu)du`
`int (u^(1/2)-7u^(-1/2)) du`
`int u^(1/2) du = u^(3/2)/(3/2) = 2/3 u^(3/2)`
`int u^(-1/2) du = u^(1/2)/(1/2) = 2u^(1/2)`
`= 2/3 u^(3/2) - 7(2u^(1/2))`
`= 2/3 u^(3/2) - 14(u^(1/2))`
`= 2/3 (x+5)^(3/2) - 14(x+5)^(1/2) + C`
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