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प्रश्न
Evaluate the following integral:
`int sqrt(2x^2 - 3) "d"x`
उत्तर
`int sqrt(2x^2 - 3) "d"x = int sqrt(2(x^2 - 3/2)) "d"x`
= `sqrt(2) int sqrt(x^2 - (sqrt(3)/2)^2) "d"x`
= `sqrt(2) [x/2 sqrt(x^2 - 3/2) - 3/((2)(2)) log |x + sqrt(x^2 - 3/2)|] + "c"`
= `sqrt(2)[x/2 sqrt((2x^2 - 3)/2) - 3/4 log |x + sqrt(x^2 - 3)/2|] + "c"`
= `sqrt(2) [(xsqrt(2x^2 - 3))/(2sqrt(2)) - 3/4 log |(sqrt(2)x + sqrt(2x^2 - 3))/sqrt(2)|] + "c"`
= `x/2 sqrt(2x^2 - 3) - (3sqrt(2))/4 log |sqrt(2x) + sqrt(2x^2 - 3)| + "k"`
Where `(3sqrt(2))/4 log sqrt(2)` is a constant
So `(3sqrt(2))/4 log sqrt(2) + "c" = "k"`
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