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t2=sinx⟹2tdt=cosxdx⟹dx=2tcosxdt.We also need to express cosx in terms of t:cosx=√1−sin2x=√1−t4.Substituting these into the integral gives:I=∫√1−t4tet⋅2t√1−t4dt.This simplifies to:I=2∫etdt. Step 3: IntegrateNow we can integrate:I=2et+C. Step 4: ...
What is the integral of cosx^3 sinx^8 dx [write cosx^3 as cosx(1-sinx^2)] Find the indefinite integral S(x - 6x^{14} + \frac {1}{8x}) dx Find the indefinite integral: int (x-5x^4 + 1/2x) dx Find the indefinite integral: 1/x ln(x^3) dx Find the indefinite integral:...
求不定积分Integral of (a*sinx + b*cosx)/(c*sinx + d*cosx) dx(sinx)'=cosx (cosx)'=-sinx,在导数里,是2个非常友好的函数,本题的分子分母结构一样,只是系数不同,可以利用这个条件,用待定系数的方法,将被积函数分解成2个容易积分的函数,求解出答案。, 视频播放量
Integrate: integral_0^pi/2 (sinx + cosx)^2 Integrate 1/sinx Evaluate the indefinite integral of sin(x) cos(x) dx using integration by parts How to integrate sqrt(1 - cos(x)) Integrate the given function. integral 5 sin^2 x dx Integrate the following: integral cos^3 2 x sin^2 2...
(1)xe^x-e^x+c(2)-xcosx+sinx+c(3)1/3x^3lnx-1/9x^3-c(4)-1/3πccos3x+1/9sin3x-c(5)1/2xsin2x⋅|1/4cos2x|c(6)xtanx+ln(cosx)+c(7)xlnx-x+c(8)x(lnx)^2-2xlnx+2x+c(9)αarctana1/2ln(a^2)1e 结果一 题目 Use integration by parts to find the integral of...
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55. f(x)=sinx,a=0,b=2πf(x)=sinx,a=0,b=2π56. f(x)=cosx,a=0,b=2πf(x)=cosx,a=0,b=2π Show Solution In the following exercises, approximate the average value using Riemann sums L100L100 and R100R100. How does your answer compare with the exact given answer?
Again, people memorize that the antiderivative of cosx is sinx. What's the antiderivative of tan? tan x = - ln|cos x| + C. What are the applications of derivatives? Applications of Derivatives in Maths Finding Rate of Change of a Quantity. Finding the Approximation Value. Finding the ...
∫cotxdx ln|sinx| + C ∫tanxdx -ln|cosx| + C ∫secxdx ln|secx + tanx| + C ∫e^u du e^u + C ∫cscxdx -ln|cscx+cotx| + C d/dx [a^x] (a^x) * ln a d/dx aᵘ aᵘ (ln a) du/dx d/dx [log a (x)] 1/(x * ln a) ∫a^x dx a^x/ln(a) + C d/dx...