નીચેનામાંથી કયું વિધાન $TRUE$ (સાચું) છે?

  • A
    $x \cdot \int \frac{dx}{x} = x \ln |x| + C$
  • B
    $x \cdot \int \frac{dx}{x} = x \ln |x| + Cx$
  • C
    $\frac{1}{\cos x} \cdot \int \cos x \, dx = \tan x + C$
  • D
    $\frac{1}{\cos x} \cdot \int \cos x \, dx = x + C$

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જો $\int \frac{x+5}{x^2+4x+5} dx = a \log(x^2+4x+5) + b \tan^{-1}(x+k) + C$ હોય,તો $(a, b, k)$ ની કિંમત શોધો.

નીચેનું સંકલન શોધો: $\int \frac{x^{3}+3 x+4}{\sqrt{x}} d x$

${F_1}(x) = \int_2^x {(2t - 5)\,dt} $ અને ${F_2}(x) = \int_0^x {2t\,dt} $ ના છેદબિંદુઓ શોધો.

$\int \sec^2 x \csc^2 x \, dx = $ . . . . . . $+ C$

$\int x \cos^2 x \, dx = $

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