જો $\int\left(\frac{1}{x}+\frac{1}{x^3}\right)\left(\sqrt[23]{3 x^{-24}+x^{-26}}\right) d x =-\frac{\alpha}{3(\alpha+1)}\left(3 x^\beta+x^\gamma\right)^{\frac{\alpha+1}{\alpha}}+C, x>0,$ $(\alpha, \beta, \gamma \in Z)$,જ્યાં $C$ એ સંકલનનો અચળાંક છે,તો $\alpha+\beta+\gamma$ ની કિંમત . . . . . . છે.

  • A
    $18$
  • B
    $19$
  • C
    $20$
  • D
    $21$

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સંકલન $\int \frac{dx}{(1 + \sqrt{x}) \cdot \sqrt{x} \sqrt{1 - x}}$ ની કિંમત શોધો (જ્યાં $c$ એ સંકલનનો અચળાંક છે)

જો $\int(x+2) \sqrt{x^2-x+2} \, dx = \frac{1}{3} f(x) + \frac{5}{8} g(x) + \frac{35}{16} h(x) + c$ હોય, તો $f(-1) + g(-1) + h\left(\frac{1}{2}\right) = $

જો $\int \frac{dx}{1-\sin^4 x} = A \tan x + B \tan^{-1}(\sqrt{2} \tan x) + C$ હોય,તો $A^2 - B^2 =$

જો $\int \frac{1}{x^4+8 x^2+9} d x = \frac{1}{k} \left[ \frac{1}{\sqrt{14}} \tan^{-1}(f(x)) - \frac{1}{\sqrt{2}} \tan^{-1}(g(x)) \right] + c$ હોય, તો $\sqrt{\frac{k}{2} + f(\sqrt{3}) + g(1)} =$

$\int \frac{dx}{4\sin^2 x + 5\cos^2 x} = $

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