\(\int \frac{x+\sin x}{1+\cos x}\) 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
\(\int_{a}^{b}\) 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)
\(\int_{-2}^{2}\) |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
\(\frac{d}{dx}\)∫f(x)dx is equal to
  • f'(x)
  • f(x)
  • f'(x’)
  • f(x) + c
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
\(\int_{0}^{\pi^{2} / 4} \frac{\sin \sqrt{y}}{\sqrt{y}}\)
  • 1
  • 2
  • \(\frac{π}{4}\)
  • \(\frac{π^2}{8}\)
\(\int_{0}^{\infty} \frac{1}{1+e^{x}}\) dx =
  • log 2
  • -log 2
  • log 2 – 1
  • log 4 – 1
\(\int_{0}^{1}\) x(1 – x) is equal to
  • \(\frac{1}{10010}\)
  • \(\frac{1}{10100}\)
  • \(\frac{1}{1010}\)
  • \(\frac{11}{10100}\)
What is the value of \(\int_{0}^{1}\) \(\frac{d}{dx}\){sin(\(\frac{2x}{1+x^2}\))}dx?
  • 0
  • π
  • -π
  • \(\frac{π}{2}\)
\(\int_{0}^{1}\) \(\frac{x}{1+x}\) dx =
  • 1 – log 2
  • 2
  • 1 + log 2
  • log 2
∫log xdx =
  • log 10.x log(\(\frac{x}{e}\)) + c
  • log e.x log(\(\frac{x}{e}\)) + c
  • (x – 1) log x + c
  • \(\frac{1}{x}\) + c
∫\(\frac{2dx}{\sqrt{1-4x^2}}\) =
  • tan (2x) + c
  • cot (2x) + c
  • cos(2x) + c
  • sin(2x) + c
Value of ∫\(\frac{dx}{\sqrt{2x – x^2}}\)
  • sin(x – 1) + c
  • sin(1 + x) + c
  • sin(1 + x²) + c
  • –\(\sqrt{2x-x^2}\) + c
0 h : 0 m : 1 s

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