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Question
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`
Solution
Let I = `int (1)/sqrt(8 - 3x + 2x^2).dx`
I = `int (1)/sqrt(2x^2 - 3x + 8).dx`
I = `1/sqrt2 int 1/sqrt(x^2 - 3/2x + 4)dx`
I = `1/sqrt2 int 1/sqrt((x^2 - 3/2x + 9/16) + 4 -9/16)dx`
I = `1/sqrt2 int 1/sqrt((x - 3/4)^2 + (sqrt(55)/4)^2`
I = `(1)/sqrt(2) log| x - (3)/(4) + sqrt((x - (3)/(4))^2 + (55/4)^2)|`
I =`(1)/sqrt(2) log| x - (3)/(4) + sqrt(x^2 - (3x)/(2) + 4)| + c`.
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