A: $\arctan (\sin x) + C$
B: $\arctan ({\sin ^2}x) + C$
C: ${\arctan ^2}(\sin x) + C$
D: $ - {\arctan ^2}(\sin x) + C$
举一反三
- $\int {{1 \over {3 + 5\cos x}}} dx = \left( {} \right)$ A: ${1 \over 4}\ln \left| {{{2\cos x + \sin x} \over {2\cos x - \sin x}}} \right| + C$ B: ${1 \over 4}\ln \left| {{{2\cos {x \over 2} + \sin {x \over 2}} \over {2\cos {x \over 2} - \sin {x \over 2}}}} \right| + C$ C: $\ln \left| {{{\cos {x \over 2} + \sin {x \over 2}} \over {\cos {x \over 2} - \sin {x \over 2}}}} \right| + C$ D: $\ln \left| {{{\cos x + \sin x} \over {\cos x - \sin x}}} \right| + C$
- 函数\(y = { { \sin x} \over x}\)的导数为（ ）. A: \( { { x\cos x - \sin x} \over { { x^2}}}\) B: \( { { x\cos x + \sin x} \over { { x^2}}}\) C: \( { { x\sin x - \cos x} \over { { x^2}}}\) D: \( { { x\sin x + \cos x} \over { { x^2}}}\)
- \( \int {\cos \ln xdx} = \)( ) A: \( {x \over 2}(\cos \ln x + \sin \ln x) + C \) B: \( {x \over 2}(\cos \ln x - \sin \ln x) + C \) C: \(- {x \over 2}(\cos \ln x + \sin \ln x) + C \) D: \(- {x \over 2}(\cos \ln x - \sin \ln x) + C \)
- 求极限\( \lim \limits_{x \to 0} { { {x^2}\sin {1 \over x}} \over {\sin x}}{\rm{ = }}\)______
- $\int {{{x\cos x} \over {{{\sin }^3}x}}} dx = \left( {} \right)$ 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$
内容
- 0
\(\lim \limits_{x \to 0} 2 { { \tan x - \sin x} \over { { {\sin }^3}x}}{\rm{ = }}\)______ 。
- 1
求微分方程[img=143x21]17da5f14490e50e.png[/img]的通解,实验命令为(). A: dsolve(D2y-2*Dy+5*y=sin(2*x),x)ans =exp(x)*sin(2*x)*C2+exp(x)*cos(2*x)*C1+1/17*sin(2*x)+4/17*cos(2*x) B: dsolve('D2y-2*Dy+5*y=sin(2*x)','x')ans =cos(2*x)*(sin(4*x)/17 - cos(4*x)/68 + 1/4) - sin(2*x)*(cos(4*x)/17 + sin(4*x)/68) + C1*cos(2*x)*exp(x) - C2*sin(2*x)*exp(x) C: dsolve(D2y-2*Dy+5*y=sin(2*x),'x','y')ans =exp(x)*sin(2*x)*C2+exp(x)*cos(2*x)*C1+1/17*sin(2*x)+4/17*cos(2*x)
- 2
求微分方程[img=364x55]17da65386dfd612.png[/img]的通解； （ ） A: - cos(2*x)*exp(x)*(x/4 - sin(4*x)/16) + C23*cos(2*x)*exp(x) + C24*sin(2*x)*exp(x) B: (3*sin(2*x)*exp(x))/32 - (sin(6*x)*exp(x))/32 - cos(2*x)*exp(x)*(x/4 - sin(4*x)/16) + C23*cos(2*x)*exp(x) + C24*sin(2*x)*exp(x) C: - sin(4*x)/16) + C23*cos(2*x)*exp(x) + C24*sin(2*x)*exp(x) D: (sin(6*x)*exp(x))/32 - cos(2*x)*exp(x)*(x/4 - sin(4*x)/16) + C23*cos(2*x)*exp(x) + C24*sin(2*x)*exp(x)
- 3
\( \lim \limits_{x \to 0} { { \sqrt {1 + x\sin x} - \cos x} \over { { {\sin }^2}{x \over 2}}} = \)______ 。
- 4
\( \int { { {\cos 2x} \over {\sin x - \cos x}}dx} = \)( ) A: \(\sin x + \cos x + C \) B: \( - \sin x + \cos x + C \) C: \( - \sin x- \cos x + C \) D: \( \sin x - \cos x + C \)