A problem from G.H. hardy`s book

Calculus Level 5

If the antiderivative, $\displaystyle \int \dfrac{dx}{1+x^4}$ is in the form

$\dfrac1{a\sqrt b} \left [\ln\left(\dfrac{1+x \sqrt b + x^2}{1-x\sqrt b + x^2} \right) + 2\tan^{-1} \left(\dfrac{x\sqrt b}{1-x^2} \right) \right ]$

find $a\times b$ .

The answer is 8.

1 solution

Akhilesh Vibhute
Jan 18, 2016

multiply and divide by 2 write that 2 as (x^2+1)-(x^2-1) separate them divide by x^2 to both numerator and denominator let u=(x^2-1)/x and v=(x^+1)/x simplify a=4 and b=2

A problem from G.H. hardy`s book

The answer is 8.

1 solution

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