answer:To integrate frac{sin^{3}x}{cos^{2}x}, we can use the identity sin^2{x} = 1 - cos^2{x}. The integral can be rewritten as follows: int frac{sin^3{x}}{cos^2{x}} dx = int frac{sin^2{x} cdot sin{x}}{cos^2{x}} dx = int frac{(1 - cos^2{x}) cdot sin{x}}{cos^2{x}} dx Now, let's make a substitution: cos{x} = t, which implies sin{x} dx = -dt. The integral becomes: -int frac{1 - t^2}{t^2} dt = -int left(frac{1}{t^2} - 1right) dt = -left(-frac{1}{t} + tright) + C = frac{1}{t} + t + C Since cos{x} = t, the final result is: int frac{sin^{3}x}{cos^{2}x} dx = frac{1}{cos{x}} + cos{x} + C This integral is now in a more concise and coherent form, with the steps clearly outlined.

answer:在经济学中，存量变量是在特定时间点可测量的，因此可以被描述为静态概念。相反，流量变量是一个动态概念，因为它是在经济中随着时间的推移来衡量的。移民指的是人们从自己的祖国移居到另一个国家，以寻找工作或寻求安全。加拿大人迁移到美国的人数被视为流量变量，因为它是时间维度的。这是因为移民数量不是在一段时间内评估的，而是在特定时间点上。因此，每年的加拿大移民到美国的人数反映了人口流动的变化，而不是一个固定不变的总量。

answer:The derivative of the function {eq}y(x) = x^2 - 3e^x {/eq} can be found using the power rule for the {eq}x^2 {/eq} term and the chain rule for the {eq}3e^x {/eq} term, due to the linearity of differentiation. Applying the rules, we get: {eq}begin{align*} y'(x) &= (x^2)' - (3e^x)' &= 2x - 3(e^x)' &= 2x - 3(e^x) &= 2x - 3e^x end{align*} {/eq}

answer:The gradient of the function f(x, y, z) is a vector composed of the partial derivatives of f with respect to x, y, and z. For the given function, the partial derivatives are: [ frac{partial f}{partial x} = 0 ] [ frac{partial f}{partial y} = z^3 cos(yz^3) ] [ frac{partial f}{partial z} = 3yz^2 cos(yz^3) ] Thus, the gradient of f is: [ nabla f = left{0, z^3 cos(yz^3), 3yz^2 cos(yz^3)right} ]