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Quiz 3
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Evaluate: ∫(2 tan x – 3 cot x)² dx
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-4tan x – cot x – 25x + C
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4 tan x – 9 cot x – 25x + C
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– 4 tan x + 9 cot x + 25x + C
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4 tan x + 9 cot x + 25x + C
Explanation
4 tan x – 9 cot x – 25x + C
Evaluate: ∫ sec²(7 – 4x)dx
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–\(\frac{1}{4}\) tan(7 – 4x) + C
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\(\frac{1}{4}\) tan(7 – 4x) + C
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\(\frac{1}{4}\) tan(7 + 4x) + C
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–\(\frac{1}{4}\) tan(7x – 4) + C
Explanation
–\(\frac{1}{4}\) tan(7 – 4x) + C
∫ \(\frac{10x^9+10^xlog_e 10}{10^x+x^{10}}\) dx is equal to
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10 – x + C
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10+ x+ C
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(10– x)+ C
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log (10+ x) + C
Explanation
log(10+ x) + C
Evaluate: ∫ sec x cosec xdx
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\(\frac{3}{5}\) tan x – 3 tan x + C
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–\(\frac{3}{5}\) tan x + 3 tan + C
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–\(\frac{3}{5}\) tan x – 3 tan + C
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None of these
Explanation
–\(\frac{3}{5}\) tanx + 3 tan + C
∫ \(\frac{a}{(1+x^2)tan^{-1}x}\) dx =
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a log |tan x| + C
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\(\frac{1}{2}\)(tanx)² + C
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a log (1 + x) + C
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None of these
Explanation
a log |tan x| + C
∫ \(\frac{cot x}{\sqrt[3]{sin x}}\) dx =
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\(\frac{-3}{\sqrt[3]{sin x}}\) + C
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\(\frac{-2}{sin^3 x}\) + C
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\(\frac{3}{sin^{1/3}x}\) + C
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None of these
Explanation
\(\frac{-3}{\sqrt[3]{sin x}}\) + C
Evaluate: ∫ \(\frac{1}{1+3sin^2x+8cos^2x}\) dx
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\(\frac{1}{6}\) tan(2 tan x) + C
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tan(2 tan x) + C
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\(\frac{1}{6}\) tan(\(\frac{2 tan x}{3}\)) + C
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None of these
Explanation
\(\frac{1}{6}\) tan(\(\frac{2 tan x}{3}\)) + C
Evaluate: ∫ \(\frac{1}{\sqrt{9+8x-x^2}}\) dx
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-sin(\(\frac{x-4}{5}\)) + C
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sin(\(\frac{x+4}{5}\)) + C
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sin
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None of these
Explanation
sin(\(\frac{x-4}{5}\)) + C
∫ \(\frac{dx}{1-cosx-sinx}\) is equal to
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log |1 + cot\(\frac{x}{2}\)| + C
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log |1 – tan\(\frac{x}{2}\)| + C
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log |1 – cot\(\frac{x}{2}\)| + C
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log |1 + tan\(\frac{x}{2}\)| + C
Explanation
log |1 – cot\(\frac{x}{2}\)| + C
Evaluate: ∫ \(\frac{1}{\sqrt{1-e^{2x}}}\) dx
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log |e + \(\sqrt{e^{-2x} – 1}\)| + C
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-log |e + \(\sqrt{e^{-2x} – 1}\)| + C
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-log |e– \(\sqrt{e^{-2x} – 1}\)| + C
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None of these
Explanation
-log |e + \(\sqrt{e^{-2x} – 1\)| + C
If ∫ \(\frac{3x+4}{x^3-2x-4}\) dx = log |x – 2| + k log f(x) + c, then
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f(x) = |x² + 2x + 2|
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f(x) = x² + 2x + 2
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k = –\(\frac{1}{2}\)
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All of these
Explanation
All of these
Evaluate: ∫ \(\frac{1-cosx}{cosx(1+cosx)}\) dx
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log|sec x + tan x| – 2 tan(x/2) + C
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log|sec x – tan x| – 2 tan(x/2) + C
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log|sec x + tan x| + 2 tan(x/2) + C
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None of these
Explanation
log|sec x + tan x| – 2 tan(x/2) + C
∫ cos(log.x)dx is equal to
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\(\frac{1}{2}\) x[cos (logx) + sin(log x)]
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x[cos (log x) + sin(log x)]
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\(\frac{1}{2}\) x[cos (log x) – sin(log x)]
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x[cos (log x) – sin(log x)]
Explanation
–\(\frac{3}{5}\) tan x + 3 tan+ C
∫ |x| dx is equal to
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\(\frac{1}{2}\) x² + C
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–\(\frac{x^2}{2}\) + C
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x|x| + C
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\(\frac{1}{2}\) x|x| + C
Explanation
\(\frac{1}{2}\) x|x| + C
∫ sin xdx is equal to
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cos x + C
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x sin x + \(\sqrt{1-x^2}\) + C
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\(\frac{1}{\sqrt{1-x^2}}\) + C
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x sin x – \(\sqrt{1-x^2}\) + C
Explanation
x sin x + \(\sqrt{1-x^2}\) + C
∫ cos (\(\frac{1}{x}\))dx equals
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x sec x + log |x + \(\sqrt{x^2-1}\)| + C
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x sec x – log |x + \(\sqrt{x^2-1}\)| + C
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-x sec x – log |x + \(\sqrt{x^2-1}\)| + C
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None of these
Explanation
x sec x – log |x + \(\sqrt{x^2-1}\)| + C
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