题目

函数 (x)=(x)^3+2(x)^2+3x+4 的不定积分是()-|||-A. ((x)^3+2(x)^2+3x+4)dx=(dfrac (1)(4))(x)^4+(dfrac (2)(3))(x)^3+(dfrac (3)(2))(x)^2+4x+C x+c-|||-B. int ((x)^3+2(x)^2+3x+4)dx=(dfrac (1)(3))(x)^3+2(x)^2+(dfrac (3)(2))x+4a+C-|||-C. int ((a)^3+2(x)^2+3x+4)dx=(dfrac (1)(4))(e)^4+(dfrac (2)(3))(a)^3+(dfrac (3)(2))(x)^2+4x-|||-D. int ((x)^3+2(x)^2+3x+4)dx=(dfrac (1)(3))(x)^3+2(x)^2+(dfrac (3)(2))x

$\begin{aligned} &函数f(x) = x^3 + 2 x^2 + 3 x + 4 的不定积分是() \\ &A.\int(x^3+2x^2+3x+4)dx =(\frac14)x^4+(\frac23)x^3+(\frac32)x^2+4x+C \\ &B.\int(x^3+2x^2+3x+4)dx=(\frac13)x^3+2x^2+(\frac32)x+4x+C \\ &\text{C}. \int(x^3+2x^2+3x+4)dx=(\frac14)x^4+(\frac23)x^3+(\frac32)x^2+4x \\ &D.\int(x^3+2x^2+3x+4)dx=(\frac13)x^3+2x^2+(\frac32)x \\ \end{aligned}$

题目解答

答案

解：

$\begin{aligned} &f(x)=x^{3}+2x^{2}+3x+4 \\ &已知\int f(x)dx=F(x)+c\\&且F(x)=f(x),又(x^{n})^{\prime}=nx^{n-1},所以\\&\int f(x)dx=\frac{x^{4}}{4}+\frac{2}{3}x^{3}+\frac{3}{2}x^{2}+4x+c \\ \end{aligned}$

所以选择：A