$\int {{{\sin 2x} \over {1 + {{\sin }^4}x}}} {\rm{d}}x = $
A: $\arctan (\sin x) + C$
B: $\arctan ({\sin ^2}x) + C$
C: ${\arctan ^2}(\sin x) + C$
D: $ - {\arctan ^2}(\sin x) + C$
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$