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Problem The value of I = d x ( a + b x 2 ) b − a x 2 I = \frac{dx}{(a+bx^2)\sqrt{b-ax^2}} I = ( a + b x 2 ) b − a x 2 d x 1 a ( a 2 + b 2 ) tan − 1 ( x a 2 + b 2 a b − a x 2 ) + C \frac{1}{\sqrt{a(a^2+b^2)}} \tan^{-1} \left( \frac{x\sqrt{a^2+b^2}}{a\sqrt{b-ax^2}} \right) + C a ( a 2 + b 2 ) 1 tan − 1 ( a b − a x 2 x a 2 + b 2 ) + C 1 ( a 2 + b 2 ) tan − 1 ( x a 2 + b 2 a b − a x 2 ) + C \frac{1}{\sqrt{(a^2+b^2)}} \tan^{-1} \left( \frac{x\sqrt{a^2+b^2}}{a\sqrt{b-ax^2}} \right) + C ( a 2 + b 2 ) 1 tan − 1 ( a b − a x 2 x a 2 + b 2 ) + C 1 a ( a 2 + b 2 ) tan − 1 ( x a 2 + b 2 a ) + C \frac{1}{\sqrt{a(a^2+b^2)}} \tan^{-1} \left( \frac{x\sqrt{a^2+b^2}}{a} \right) + C a ( a 2 + b 2 ) 1 tan − 1 ( a x a 2 + b 2 ) + C Browse the problem library