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प्रश्न
Integrate the following functions w.r.t. x : `sqrt(2x^2 + 3x + 4)`
उत्तर
Let I = `int sqrt(2x^2 + 3x + 4).dx`
= `sqrt(2) int sqrt(x^2 + 3/2 x + 2).dx`
= `sqrt(2) int sqrt((x^2 + 3/2x + 9/16) - 9/16 + 2).dx`
= `sqrt(2) int sqrt((x + 3/4)^2 + (sqrt(23)/4)^2).dx`
= `sqrt(2)[((x + 3/4))/(2) sqrt((x + 3/4)^2 + (sqrt(23)/4)^2 ) + ((23/16))/(2)log|(x + 3/4) + sqrt((x + 3/4)^2 + (sqrt(23)/4)^2)|] + c`
= `ssqrt(2)[((4x + 3)/8) sqrt(x^2 + 3/2x + 2) + (23)/(32)log|(x + 3/4) + sqrt(x^2 + 3/2x + 2)|] + c`.
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