Calculus is Irresistible!

Calculus Level 5

If I = ∫ a x 2 + 2 b x + c ( A x 2 + 2 B x + C ) 2 d x \text{I = } \int \frac{ax^{2} +2bx+c}{(Ax^{2}+2Bx+C)^{2}}dx (where B 2 > A C B^{2} > AC ) is a rational function then it is possible to derive the relation α B b = β A c + γ a C . \alpha Bb = \beta Ac + \gamma aC.

Find the value of α + β 2 + γ 3 \alpha +\beta^{2} +\gamma^{3} , where α \alpha is a prime number.

Credits: Problems in Calculus by Sameer Bansal.


The answer is 4.

Hrithik Thakur by Hrithik Thakur , 19, India

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1 solution

Hrithik Thakur
Oct 7, 2019

Here, I have posted an image of the solution. Apologies, if you have any issues with the image clarity.

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