∫x² sin x³ dx =
  • \(\frac{1}{3}\) cos x³ + c
  • –\(\frac{1}{3}\) cos x + c
  • \(\frac{-1}{3}\) cos x³ + c
  • \(\frac{1}{2}\) sin² x³ + c
∫tan √xdx is equal to
  • (x + 1)tan √x – √x + C
  • x tan √x – √x + C
  • √x – x tan √x + C
  • √x – (x + 1)tan √x + C
∫e(\(\frac{1-x}{1+x^2}\))² dx is equal to
  • \(\frac{e^x}{1+x^2}\) + C
  • –\(\frac{-e^x}{1+x^2}\) + C
  • \(\frac{e^x}{(1+x^2)^2}\) + C
  • \(\frac{-e^x}{(1+x^2)^2}\) + C
If ∫\(\frac{dx}{(x+2)(x^2+1)}\) = a log |1 + x²| + b tan x + \(\frac{1}{5}\) log |x + 2| + C, then
  • a = \(\frac{-1}{10}\), b = \(\frac{-2}{5}\)
  • a = \(\frac{1}{10}\), b = \(\frac{-2}{5}\)
  • a = \(\frac{-1}{10}\), b = \(\frac{2}{5}\)
  • a = \(\frac{1}{10}\), b = \(\frac{2}{5}\)
∫ \(\frac{x^3}{x+1}\) is equal to
  • x + \(\frac{x^2}{2}\) + \(\frac{x^3}{3}\) – log |1 – x| + C
  • x + \(\frac{x^2}{2}\) – \(\frac{x^3}{3}\) – log |1 – x| + C
  • x + \(\frac{x^2}{2}\) – \(\frac{x^3}{3}\) – log |1 + x| + C
  • x + \(\frac{x^2}{2}\) + \(\frac{x^3}{3}\) – log |1 + x| + C
If ∫\(\frac{x^3dx}{\sqrt{1+x^2}}\) = a(1 + x²)+ b\(\sqrt{1 + x^2}\) + C, then
  • a = \(\frac{1}{3}\), b = 1
  • a = \(\frac{-1}{3}\), b = 1
  • a = \(\frac{-1}{3}\), b = -1
  • a = \(\frac{1}{3}\), b = -1
Evaluate: ∫(2 tan x – 3 cot x)² dx
  • -4tan x – cot x – 25x + C
  • 4 tan x – 9 cot x – 25x + C
  • – 4 tan x + 9 cot x + 25x + C
  • 4 tan x + 9 cot x + 25x + C
Evaluate: ∫ sec²(7 – 4x)dx
  • –\(\frac{1}{4}\) tan(7 – 4x) + C
  • \(\frac{1}{4}\) tan(7 – 4x) + C
  • \(\frac{1}{4}\) tan(7 + 4x) + C
  • –\(\frac{1}{4}\) tan(7x – 4) + C
∫ \(\frac{10x^9+10^xlog_e 10}{10^x+x^{10}}\) dx is equal to
  • 10 – x + C
  • 10+ x+ C
  • (10– x)+ C
  • log (10+ x) + C
Evaluate: ∫ sec x cosec xdx
  • \(\frac{3}{5}\) tan x – 3 tan x + C
  • –\(\frac{3}{5}\) tan x + 3 tan + C
  • –\(\frac{3}{5}\) tan x – 3 tan + C
  • None of these
Evaluate: ∫ \(\frac{1}{\sqrt{9+8x-x^2}}\) dx
  • -sin(\(\frac{x-4}{5}\)) + C
  • sin(\(\frac{x+4}{5}\)) + C
  • sin
  • None of these
Evaluate: ∫ \(\frac{1}{\sqrt{1-e^{2x}}}\) dx
  • log |e + \(\sqrt{e^{-2x} – 1}\)| + C
  • -log |e + \(\sqrt{e^{-2x} – 1}\)| + C
  • -log |e– \(\sqrt{e^{-2x} – 1}\)| + C
  • None of these
If ∫ \(\frac{3x+4}{x^3-2x-4}\) dx = log |x – 2| + k log f(x) + c, then
  • f(x) = |x² + 2x + 2|
  • f(x) = x² + 2x + 2
  • k = –\(\frac{1}{2}\)
  • All of these
∫ cos(log.x)dx is equal to
  • \(\frac{1}{2}\) x[cos (logx) + sin(log x)]
  • x[cos (log x) + sin(log x)]
  • \(\frac{1}{2}\) x[cos (log x) – sin(log x)]
  • x[cos (log x) – sin(log x)]
∫ |x| dx is equal to
  • \(\frac{1}{2}\) x² + C
  • –\(\frac{x^2}{2}\) + C
  • x|x| + C
  • \(\frac{1}{2}\) x|x| + C
∫ sin xdx is equal to
  • cos x + C
  • x sin x + \(\sqrt{1-x^2}\) + C
  • \(\frac{1}{\sqrt{1-x^2}}\) + C
  • x sin x – \(\sqrt{1-x^2}\) + C
∫ cos (\(\frac{1}{x}\))dx equals
  • x sec x + log |x + \(\sqrt{x^2-1}\)| + C
  • x sec x – log |x + \(\sqrt{x^2-1}\)| + C
  • -x sec x – log |x + \(\sqrt{x^2-1}\)| + C
  • None of these
∫\(\frac{dx}{1+\cos x}\) =
  • tan \(\frac{x}{2}\) + k
  • \(\frac{1}{2}\) tan \(\frac{x}{2}\) + k
  • 2 tan \(\frac{x}{2}\) + k
  • tan² \(\frac{x}{2}\) + k
∫\(\frac{\cos 2x dx}{(\sin x+\cos x)^2}\) =
  • log | sin x + cos x | + c
  • log | sin x – cos x | + c
  • –\(\frac{1}{\sin x+\cos x}\) + c
  • \(\frac{1}{(\sin x+\cos x)^2}\)
∫\(\frac{(1+\log x)^2}{1+x^2}\) dx =
  • \(\frac{1}{3}\)(1+log)³ + c
  • \(\frac{1}{2}\)(1+log)² + c
  • log (log 1 + x) + 2
  • None of these
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