\( \int {\csc x(\csc x - \cot x)dx} = \)( )
A: \( - \cot x - \csc x + C \)
B: \( - \cot x + \csc x + C \)
C: \( \cot x + \csc x + C \)
D: \( \cot x -\csc x + C \)
A: \( - \cot x - \csc x + C \)
B: \( - \cot x + \csc x + C \)
C: \( \cot x + \csc x + C \)
D: \( \cot x -\csc x + C \)
B
举一反三
- \( \int {\sec xdx} \)=( )。 A: \( \ln \left| {\csc x + \tan x} \right| + C \) B: \( \ln \left| {\sec x + \cot x} \right| + C \) C: \( \ln \left| {\sec x + \tan x} \right| + C \) D: \( \ln \left| {\csc x + \cot x} \right| + C \)
- 求函数[img=192x40]17da653862ff7b6.png[/img]的导数； ( ) A: cos(x)/sin(x) - cot(x)*(cot(x)^2 + 1) B: cos(x)/sin(x) C: cot(x)*(cot(x)^2 + 1) D: cos(x)/sin(x) - cot(x)*(cot(x)^2 + 1)+cot(x)
- \(\int { { {\sec }^{3}}xdx}\)=( ) A: \(\frac{1}{2}\sec x\cot x-\frac{1}{2}\ln \left| \sec x+\tan x \right|+C\) B: \(\frac{1}{2}\sec x\tan x+\frac{1}{2}\ln \left| \sec x+\tan x \right|+C\) C: \(-\frac{1}{2}\csc x\tan x+\frac{1}{2}\ln \left| \sec x-\cot x \right|+C\) D: \(-\frac{1}{2}\sec x\tan x-\frac{1}{2}\ln \left| \csc x+\tan x \right|+C\)
- 函数\( y = \ln \cos x\)的导数为（ ）. A: \(\tan x\) B: \( - \tan x\) C: \(\cot x\) D: \(- \cot x\)
- 函数\(y = \ln \sin x\)的导数为（ ）. A: \( - \cot x\) B: \(\cot x\) C: \(- \tan x\) D: \(\tan x\)
内容
- 0
已知\( y = \ln (\sin x) \)，则\( y' \)为（ ）. A: \( {1 \over {\sin x}} \) B: \( {1 \over {\cos x}} \) C: \( \cot x \) D: \( - \cot x \)
- 1
下列函数组线性无关的是( ) A: $\sin<br/>2x, \sin x\cos x$ B: $\dfrac{\tan^2<br/>x}{2}, \sec^2 x-1$ C: $\cot^2<br/>x, \dfrac{\csc^2 x-1}{3}$ D: $e^{ax},<br/>e^{bx} (a\neq b)$
- 2
$\int {{{x\cos x} \over {{{\sin }^3}x}}} dx = \left( {} \right)$ A: $ - {x \over {2{{\sin }^2}x}} - {1 \over 2}\tan x + C$ B: $ - {x \over {2{{\sin }^2}x}} - {1 \over 2}\cot x + C$ C: $ - {x \over {2{{\cos }^2}x}} - {1 \over 2}\cot x + C$ D: $ - {x \over {2{{\cos }^2}x}} - {1 \over 2}\tan x + C$
- 3
lim(2-e^sinx)^cotπx(x趋近于0）
- 4
\( \lim \limits_{x \to {0^ + }} {\left( {\cot x} \right)^ { { 1 \over {\ln x}}}} \)=_____ ______