第一个注意到分母可以变成【3+cos(2x)】/2而正好sin(2x)dx=-dcos(2x)/2题目就转化为-∫dcos(2x)/【3+cos(2x)】 2022-01-23 12:134回复 晓之车高山老师 其实up表达的意思就是,被积函数某个地方稍有改动,对应不定积分表达式就可能有很大的变化,甚至完全不同 2022-01-24 03:072回复 QNのstarlake up主...
Substitute backu=xt=x1(−cos(xt)) Simplify=−x1cos(xt) Add a constant to the solution=−x1cos(xt)+C Popular Examples Frequently Asked Questions (FAQ) What is the integral of sin(xt) ? The integral of sin(xt) is -1/x cos(xt)+C...
What is the antiderivative of the integral of (5x + 3)/(x^3 - 2x^2 - 3x) dx? What is the antiderivative of the integral of sec^3(1 - 2x) dx? What is the integral of sin^7 x cos^5 x dx? integral 1/x^2(x^2 + 1)^2 dx Integral dx/x^2 - 2x + 10 Integral of tan...
∫sin3(x)cos5(x)dx Integration in Calculus: Integration techniques can be used to find antiderivatives of a trigonometric function. Sometimes trigonometric identities may be needed to do so. To solve this problem, we'll use the trig-identity(sin2x=1−cos2x)and then we'll appl...
Evaluate the integral: \int \sqrt{\frac{1-3x}{1+3xdx Evaluate the integral of \int \cos 4(4t)\sin3(8t). Evaluate the integral \int \frac{dx}{x\sqrt{1+\ln^2x Evaluate the integral: \int (2 - 2\cos^{2} x) dx Evaluate the integral. \int \frac{dx}{x(x^4+1)} ...
{eq}\displaystyle \int_{0}^{\frac{\pi }{2}}\sin ^{3}\ x\cos ^{2}\ x \ dx {/eq} Compute the indefinite integral: {eq}=\displaystyle... Learn more about this topic: Applying the Rules of Differentiation to Calculate Derivatives ...
Let ( u_1=2x). Then ( du_1=2dx), so ( 1/2du_1=dx). Rewrite using ( u_1) and ( d)( u_2).( 1/2∫ (sin)(u_2)du_2)The integral of ( (sin)(u_2)) with respect to ( u_2) is ( -(cos)(u_2)).( 1/2(-(cos)(u_2)+C))Simplify.( -((cos)(u_2))/2...
The list of basic integral formulas are ∫ 1 dx = x + C ∫ a dx = ax+ C ∫ xndx = ((xn+1)/(n+1))+C ; n≠1 ∫ sin x dx = – cos x + C ∫ cos x dx = sin x + C ∫ sec2x dx = tan x + C ∫ csc2x dx = -cot x + C ...
If f(x) is the integral of (2 sin x - sin 2x )/(x ^ 3 ) , where x ne 0, then find lim (x to 0) f' (x) .
Find an antiderivative (or integral) of the following cos 3x (ii)3x2+4x3(iii)(ax+b)2(iv)sin2x−4e3x View Solution Integrate the following :sinxsin(cosx) View Solution Integrate the following:3cosec2x+2sin3x) View Solution Integrate the following w.r.t.x. ...