Evaluate: `intsqrt(16 x^2+25) dx`

1.	Evaluate: `intsqrt(16 x^2+25) dx`
Answer» We know that `intsqrt(x^(2)+a^(2))dx=(x)/(2)sqrt(x^(2)+a^(2))+(a^(2))/(2)log\|x+sqrt(x^(2)+a^(2))\|+C`. `thereforeintsqrt(16x^(2)+25)dx=4int{sqrt(x^(2)+(25)/(16))}dx=4int{sqrt(x^(2)+((5)/(4))^(2))}dx` `=4{(x)/(2)sqrt(x^(2)+(25)/(16))+(25)/(32)log\|x+sqrt(x^(2)+(25)/(16))\|}+C` `=(x)/(2)sqrt(16x^(2)+25)+(25)/(8)log\|x+sqrt(x^(2)+(25)/(16))\|+C`.

Discussion

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