\(\int \frac{x+\sin x}{1+\cos x}\) dx is equal to
  • log |1 + cos x | + c
  • log | x + sin x | + c
  • x – tan + c
  • x. tan \(\frac{x}{2}\) + c
∫1.dx =
  • x + k
  • 1 + k
  • \(\frac{x^2}{2}\) + k
  • log x + k
∫\(\frac{dx}{√x}\) =
  • √x + k
  • 2√x + k
  • x + k
  • \(\frac{2}{3}\)x + k
∫\(\frac{dx}{1+cos x}\) =
  • tan \(\frac{x}{2}\) + k
  • \(\frac{1}{2}\) tan \(\frac{x}{2}\) + k
  • 2 tan \(\frac{x}{2}\) + k
  • tan² \(\frac{x}{2}\) + k
\(\int_{a}^{b}\) x dx =
  • tan \(\frac{x}{2}\) + k
  • \(\frac{1}{2}\) tan \(\frac{x}{2}\) + k
  • 2 tan \(\frac{x}{2}\) + k
  • tan² \(\frac{x}{2}\) + k
If x > a, ∫\(\frac{dx}{x^2-a^2}\) =
  • \(\frac{2}{2a}\) log \(\frac{x-a}{x+a}\) + k
  • \(\frac{2}{2a}\) log \(\frac{x+a}{x-a}\) + k
  • \(\frac{1}{a}\) log(x² – a²) + k
  • log(x + \(\sqrt{x^2-a^2}\) + k)
∫\(\frac{cos 2x dx}{(sinx+cosx)^2}\) =
  • –\(\frac{1}{sinx+cosx}\) + c
  • log | sin x + cos x | + c
  • log | sin x – cos x | + c
  • \(\frac{1}{(sinx+cosx)^2}\)
∫\(\frac{(1+logx)^2}{1+x^2}\) dx =
  • \(\frac{1}{3}\)(1+log)³ + c
  • \(\frac{1}{2}\)(1+log)² + c
  • log (log 1 + x) + 2
  • None of these
\(\int_{0}^{1}\frac{(tan^{-1}x)^2}{1+x^2}\) dx =
  • 1
  • \(\frac{π^2}{64}\)
  • \(\frac{π^2}{192}\)
  • None of these
\(\int_{-2}^{2}\) |x|dx =
  • 0
  • 2
  • 1
  • 4
∫\(\frac{x^4+1}{x^2+1}\) dx is equal to
  • \(\frac{x^3}{3}\) + x + tan x + c
  • \(\frac{x^3}{3}\) – x + tan x + c
  • \(\frac{x^3}{3}\) + x + 2tan x + c
  • \(\frac{x^3}{3}\) – x + 2tan x + c
∫(√x + \(\frac{1}{√x}\)) dx =
  • \(\frac{1}{x}\) x+ 2x+ c
  • \(\frac{2}{3}\) x+ \(\frac{1}{2}\)x+ c
  • \(\frac{2}{3}\) x+ 2x+ c
  • \(\frac{3}{2}\) x+ \(\frac{1}{2}\)x+ c
∫\(\frac{sin^2x-cos^2x}{sin^2xcos^2x}\) dx is equal to
  • tan x + cos x + c
  • tan x + cosec x + c
  • tan x + cot x + c
  • tan x+ sec x + c
\(\frac{d}{dx}\)∫f(x)dx is equal to
  • f'(x)
  • f(x)
  • f'(x’)
  • f(x) + c
What is the value of \(\int_{0}^{\pi / 2}\) \(\frac{\sqrt{tan x}}{\sqrt{tan x}+\sqrt{cot x}}\) dx?
  • \(\frac{π}{2}\)
  • \(\frac{π}{4}\)
  • \(\frac{π}{8}\)
  • None of these
What is the value of \(\int_{0}^{\pi / 2}\) \(\frac{sinx – cos x}{1+sin xcos x}\) dx?
  • 1
  • \(\frac{π}{2}\)
  • 0
  • –\(\frac{π}{2}\)
What is the value of \(\int_{\pi / 6}^{\pi / 3}\) \(\frac{dx}{sin2x}\)?
  • \(\frac{1}{2}\) log(-l)
  • log(- 1)
  • log 3
  • log √3
What is the value of \(\int_{-1}^{1}\) sin³ x cos² xdx?
  • 0
  • 1
  • \(\frac{1}{2}\)
  • 2
What is the value of \(\int_{1}^{e} \frac{1+\log x}{x}\) dx?
  • \(\frac{3}{2}\)
  • \(\frac{1}{2}\)
  • e
  • \(\frac{1}{e}\)
\(\int_{-\pi / 2}^{\pi / 2}\) sin xdx =
  • -1
  • 0
  • 1
  • None of these
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