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Question
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Solution
I = `int1/sqrt(3x^2 + 5x + 7)dx`
I = `1/sqrt3 int 1/sqrt(x^2 + (5x)/3 + 7/3)dx`
I = `1/sqrt3 int 1/sqrt((x^2 + (5x)/3 + 25/36) + (7/3 - 25/36))dx`
I = `1/sqrt3 int 1/sqrt((x^2 + (5x)/3 + (5/6)^2) + (59/36)).dx`
I = `1/sqrt3 int 1/sqrt((x + 5/6)^2 + (sqrt59/6)^2)dx`
I = `1/sqrt3 log |(x + 5/6) +sqrt((x + 5/2)^2 + (sqrt59/6)^2)| + c` ....`int1/sqrt(x^2 + a^2)dx = log|x + sqrt(x^2 + a^2)| + c`
I = `1/sqrt3 . log|(x + 5/6) + sqrt(x^2 + (5x)/3 + 7/3)| + c`
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