∫xe^（x^2）dx=（ ）
A: 1/2（e^（x^2））
B: 1/2（e^（x^2））+C
C: -1/2（e^（x^2））
D: -1/2（e^（x^2））十C
A: 1/2（e^（x^2））
B: 1/2（e^（x^2））+C
C: -1/2（e^（x^2））
D: -1/2（e^（x^2））十C
举一反三
- 若\( \int {f(x)dx = {x^2} + C} \)，则\( \int {xf(1 - {x^2})dx = } \)( ) A: \( 2{(1 - {x^2})^2} + C \) B: \( - {1 \over 2}{(1 - {x^2})^2} + C \) C: \( {1 \over 2}{(1 - {x^2})^2} + C \) D: \( - 2{(1 - {x^2})^2} + C \)
- 求方程$y\frac{{{d}^{2}}y}{d{{x}^{2}}}-(\frac{dy}{dx})^{2}=0$的通解： A: $y={{C}_{1}}{{e}^{-{{C}_{2}}x}}$ B: $y={{C}_{1}}{{e}^{-{{C}_{2}}{{x}^{2}}}}$ C: $y={{C}_{1}}x{{e}^{-{{C}_{2}}{{x}^{2}}}}$ D: $y={{C}_{1}}{{e}^{{{C}_{2}}x}}$
- 方程${{x}^{2}}{{y}^{''}}-(x+2)(x{{y}^{'}}-y)={{x}^{4}}$的通解是( ) A: $y={{C}_{1}}x+{{C}_{2}}{{e}^{x}}-(\frac{1}{2}{{x}^{3}}+{{x}^{2}})$ B: $y={{C}_{1}}x+{{C}_{2}}{{e}^{x}}-(\frac{1}{2}{{x}^{3}}+{{x}^{4}})$ C: $y={{C}_{1}}x+{{C}_{2}}x{{e}^{x}}-(\frac{1}{2}{{x}^{3}}+{{x}^{4}})$ D: $y={{C}_{1}}x+{{C}_{2}}x{{e}^{x}}-(\frac{1}{2}{{x}^{3}}+{{x}^{2}})$
- 设\(z = \int_ { { x^2}}^y { { e^t}\sin t} dt\)，则\({z_{xx}=}\) A: \(2{e^ { { x^2}}}\left[ {\left( {1 + 2{x^2}} \right)\sin {x^2} + 2{x^2}\cos {x^2}} \right]\) B: \( - 2{e^ { { x^2}}}\left[ {\left( {1 + 2{x^2}} \right)\sin {x^2} - 2{x^2}\cos {x^2}} \right]\) C: \( - 2{e^ { { x^2}}}\left[ {\left( {1 + 2{x^2}} \right)\sin {x^2} + 2{x^2}\cos {x^2}} \right]\) D: \( - 2{e^ { { x^2}}}\left[ {\left( {1 + 2{x^2}} \right)\cos {x^2} + 2{x^2}\sin {x^2}} \right]\)
- 求函数[img=148x49]17da6537a5eee98.png[/img]的导数； ( ) A: 1/(x^2*(2/x^2 + 1)) B: -1/(x^2*(2/x^2 + 1)) C: (x^2*(2/x^2 + 1)) D: -1/(x^2*(2/x^2 + 1))+2/x^2 + 1