2. This integral is known as the Sine Integral, denoted as Si(x).3. The Sine Integral is defined as: Si(x)=∫x0sin(t)tdt4. Therefore, the indefinite integral can be expressed in terms of the Sine Integral function: ∫sin(x)xdx=Si(x)+C where C is the constant of integration....
Answer to: Evaluate the integral: integral sin(square root x) dx / square root x. By signing up, you'll get thousands of step-by-step solutions to...
du/dx=−sin(x)du/dx=−sin(x) −du=sin(x)dx−du=sin(x)dx ∫sin3(x)cos2(x)dx=−∫(1−u2)u2du∫sin3(x)cos2(x)dx=−∫(1−u2)u2du ∫sin3(x)cos2(x)dx=∫(u4−u2)du∫sin3(x)cos2(x)dx=∫(u4−u2)du ...
如果我们要求解\int\frac{\sin(x)}{x}dx，这个积分是比较经典的积分，也称为“无穷小量的积分”。这个积分并没有一个标准的、封闭形式的表达式，但是它的结果可以表示为特殊函数——Sine Integral函数。要求解这个积分，我们可以采用不同的方法。其中一种常用的方法是将被积函数在x=0处进行泰勒展开，然后利用幂...
Integral of sin(x)^3 by x: cos(x)^3/3-cos(x)+C To compute the integral ofsin3(x)with respect tox, follow these steps: 1.Use the identity forsin3(x): This can be rewritten as: 2.Split the integral: 3.Compute the first integral: ...
Answer to: Determine the integral: Integral sin x ln(1+sin x) dx By signing up, you'll get thousands of step-by-step solutions to your homework...
I=2∫10xarcsinx1−x4−−−−−√dx=∫10(arcsin2x)′x1+x2−−−−−√dxI=2∫01xarcsinx1−x4dx=∫01(arcsin2x)′x1+x2dx =π28−∫10arcsin2x(1+x2)3/2dx=π28−∫01arcsin2x(1+x2)3/2dx We can expand into power series the integral, we...
∫sin2(x)dx=∫12(1−cos(2x))dx∫sin2(x)dx=∫12(1−cos(2x))dx =12∫dx−12∫cos(2x)dx=12∫dx−12∫cos(2x)dx =12x−14sin(2x)+C=12x−14sin(2x)+C Example 2Evaluate the integral ∫[sin2(x)−16sin6(x)]dx∫[sin2(x)−16sin6(x)]...
Integral∫ sinxdx= - cosx+C Euler's formulasinx= (eix-e-ix) / 2i Inverse sine function Thearcsineof x is defined as the inverse sine function of x when -1≤x≤1. When the sine of y is equal to x: siny=x Then the arcsine of x is equal to the inverse sine function of x,...
不定积分计算器可以用分析整合的方法,计算出一个给定变量的函数的不定积分(原函数)。它也可以画出函数和它的原函数的图像。请注意,计算的不定积分属于一类函数F(x) C,其中C是任意常数。不定积分计算器解析表达式,应用积分法则并化简最终结果。因此,积分计算的最终结果可能与常数的预期结果不同。