局限性:仅适用于u求导后归零的情况(如多项式),不适用于循环结构(如∫eˣsinx dx)。 依赖经验:需正确选择u和dv,否则可能增加计算复杂度。应用场景多项式与指数/三角函数乘积的积分 如∫x⁴cos(2x)dx、∫x²e⁻ˣdx等。 工程与物理学问题 振动分析、电路微分方程求解...
那么,哪个函数是u(x),哪个函数是v(x)呢? 对比公式,u(x)应该是在微分符号前面的一个函数,而v(x)应该是在微分符号后面的,而xsinx dx这个式子中,有两个函数都在微分符号的前面。 所以,我们要做的第一步,就是把其中的一个函数...
How can I integrate e^-x sinx using parts? I've got a function \int e^{-x}sinx dx From what I know, only functions which has one or more products with a finite number of successive differentials can be evaluated using integration by parts. Because for \int v du in our choice of ...
∫π0f∞(x)dx=∫π0−x+Sa(x)dx=∫π0−xdx+∫π0Sa(x)dx=−π22+(πSa(π)−0Sa(0)−∫Sa(π)Sa(0)y−sinydy)=−π22+(π2−∫π0y−sinydy)=−π22+(π2−[y22+cosy]π0)=2.∫0πf∞(x)dx=∫0π−x+Sa(x)dx=∫0π−xdx...
{eq}\displaystyle\int x^n\ dx=\dfrac{x^{n+1}}{n+1}+c\\\ \displaystyle\int sinx\ dx=-cosx+c\\\ \displaystyle\int cosx\ dx=sinx+c\\\ \displaystyle\int \dfrac{1}{x}dx=ln\left | x \right |+c\\\ {/eq} Answer and Expl...
Let y = (sinx)^(e^-x + 4x^3), then dy/dx = (e^-x + 4x^3)(sinx)^(e^-x + 4x^3 -1)cosx a. True b. False f(z) = ln z satisfies Cauchy-Riemann equations in polar form. True or false? Let f(x)>0 . If \int _1^{\infty} f(x)dx conver...
Use integration by parts to evaluate ##\int \sin^{-1}x \, dx## Let ##U=\sin^{-1}x,\quad{dV=dx}## Then ##dU=dx/\sqrt{1-x^2},\quad{V=x}## ##=x\sin^{-1}x-\int \frac{x}{\sqrt{1-x^2} \, dx}## Let ##u=1-x^2##... mcastillo356 Thread Nov 2, 2023 ...
Prove that limn→∞∫30(√sinxn+x+1)dxn→∞∫03(sinxn+x+1)dx exists and evaluate it 1 How to construct a counterexample to limn→∞∫10fn(x)dx=∫10f(x)dxlimn→∞∫01fn(x)dx=∫01f(x)dx 19 On the integral ∫π0sin(x+sin(x+sin(x+⋯)))dx∫0...
∫ x^n dx = x^n+1 * 1/(n+1) + c for n≠-1this is the Reverse Power Rule(add one to the exponent, then multiply by reciprocal) ∫ 1/x dx = ln|x| + C ∫ e^x dx = e^x + C ∫ a^x dx = 1/ln(a) * a^x + C ∫ cosx dx = sinx + C ∫ sinx dx = -cosx...
ln|x| + c ∫ x⁻¹dx = ? a×/ln(a) + c ∫ a×dx = ? e× + c ∫ e×dx = ? 1 sin²x + cos²x = ? sec²x tan²x + 1 = ? csc²x 1 + cot²x = ? -cosx + c ∫ sinxdx = ? sinx + c ∫ cosxdx = ? -ln|cosx| + c ∫ tanxdx = ? ln|sin...