Topic: Integration by Substitution
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How to Integrate by Substitution
The method of integration by substitution for indefinite integrals involves changing a variable say x of an integrand to another variable u. You denote the relationship between x and u as ∫ f (g (x)) g′ (x) dx = ∫ f (u) du. You integrate by... Read More »
Source: http://www.ehow.com/how_2258560_integrate-substitution.html
How to Integrate a Trigonometrical Integrand Using U-Substitution
The Example problem that we will be using has symbols that are better shown in the Image, so please click on the Image to see the Integration Problem. To use U-substitution to solve this Integral, we first set u = sin(2x), then find the der... Read More »
Source: http://www.ehow.com/how_5396369_integrate-trigonometrical-integra...
How does the method of substitution work for definite integrals?
You mean 'u' subsititution? It helps you get the anti-derivative easier, therefore allowing you to input values to get the definite integral. I hope I helped :D Read More »
Source: http://wiki.answers.com/Q/How_does_the_method_of_substitution_wor...
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Integration by Substitution
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i love wikipedia! According to wiki: In calculus, integration by substitution is a method for finding antiderivatives and integrals. Using the fundamental theorem of calculus often requires finding an antiderivative. For this and other reas...
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Source: http://wiki.answers.com/Q/How_is_integration_through_substitution...
This Article will show How to Evaluate an Integral, that seems to be very Difficult to Integrate, but by using a change of variable, from the variable x to the variable u, and a with prior knowledge of the Derivative of Inverse Trigonometri...
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Source: http://www.ehow.com/how_5425392_use-involves-inverse-trigonometri...
let w = { (2/a) - a } to get to w dw
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Source: http://answers.yahoo.com/question/index?qid=20120226194505AABmeiX
∫ ln²x dx = let: lnx = t x = e^t dx = e^t dt thus, substituting: ∫ ln²x dx = ∫ t² e^t dt = let: t² = u → 2t dt = du e^t dt = dv → e^t = v then, integrating by parts: ∫ u dv = u v - ∫ v du ∫ t² e^t dt = t² e^t - ∫ e^t 2t dt = t² e^t - 2 ∫ t ...
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Source: http://answers.yahoo.com/question/index?qid=20100224141900AAY09wM
∫ [1 /(1 + x²)²] dx = x = tan u ↔ u = arctanx dx = sec²u du substituting, you get: ∫ [1 /(1 + x²)²] dx = ∫ [1 /(1 + tan²u)²] sec²u du = recall that 1 + tan²u = sec²u: ∫ [1 /(sec²u)²] sec²u du = that simplifies into: ∫ [1 /(sec²u)] du = ∫ (1...
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Source: http://uk.answers.yahoo.com/question/index?qid=20090421131131AAvp...
∫³√(x³+5) *x⁵ dx= =∫³√(x³+5) *x³ * x² dx= =(1/3)∫³√(x³+5) *x³ d(x³)= =(1/3)∫³√(x³+5) *x³ d(x³+5)= Let v=x³+5 =(1/3)∫³√v *(v-5) dv= =(1/3)∫ v^(1/3+1) - 5v^(1/3) dv= =(1/3)∫ v^(4/3) dx - (5/3)∫ v^(1/3) dv= =(1/3)v^(4/3+1)/(4/3+1) - (5/3)v^(1/...
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Source: http://answers.yahoo.com/question/index?qid=20110909002932AAo9uzy
