Trigonometry (x inradians)∫cos(x) dxsin(x) + C ∫sin(x) dx-cos(x) + C ∫sec2(x) dxtan(x) + C RulesFunction Integral Multiplication by constant∫cf(x) dxc∫f(x) dx Power Rule (n≠−1)∫xndxxn+1n+1+ C Sum Rule∫(f + g) dx∫f dx +∫g dx ...
Examples∫215x2 cos(x3) dx Try u = x3, therefore, du = 3x2dx.x2dx = (1/3) duWe must change the limits of integration, the new values come from u = x3, therefore when x= 1, u = 1 and when x= 2, u = 8. The integral becomes,...
Evaluate the following integration int 2^(x)*e^(x)*dx 03:02 Evaluate : int (e^(5x)+e^(3x))/(e^(x)+e^(-x)) dx 01:28 int (e^(xloga)+e^(alogx))dx 01:39 Evaluate: int(1+cos4x)/(cotx-tanx)\ dx 04:39 Evaluate int tanx tan 2x tan 3x dx. 02:12 Evaluate the follo...
Integration by a {eq}\int {\ln (\cos x)\tan xdx} {/eq} Indefinite Integration: Let y = f(x) be any function of x. Then, the indefinite integral with respect to x is given by: {eq}\displaystyle I = \int {ydx} = \int {f(x)dx} {/eq} Required formulas: {eq}\displ...
(u integral v) minus integral of (derivative u, integral v)Let's try some more examples:Example: What is∫ln(x)/x2 dx ? First choose u and v: u = ln(x) v = 1/x2 Differentiate u: ln(x)' = 1x Integrate v: ∫1/x2 dx = ∫x-2 dx = −x-1 = −1x (by the powe...
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{eq}\int_{0}^{2}{\int_{0}^{\sqrt{4-{{x}^{2}}}{{{\tan }^{-1}}\left( \frac{y}{x} \right)}dy}dx {/eq} First Quadrant: The first quadrant of the plane is composed by the infinite points of the plane that...
If f(x) and g(x) are two functions, then ∫f(x)g(x)dx=f(x)( integral of g(x))−∫( integral of g(x))(Differential of f(x))dx How to choose functions f(x) and g(x): If we have product of two functions whose integral is not know...
A growing number of leaders in towns and cities across the United States have embraced policies encouraging receptivity and integration of immigrant populations. This article examines this phenomenon and how communities are seeking greater immigrant integration. To do this, we describe immigration ...
Example 9:Evaluate ∫xsec2x dx. Example 10:Evaluate ∫x4Inx dx. Example 11:Evaluate ∫ arctanx dx. Integrals involving powers of the trigonometric functions must often be manipulated to get them into a form in which the basic integration formulas can be applied. It is extremely important for...