Use integration by parts to find the integral of:[Hint: In (7) write lnx as 1lnx and in (9) write arctanxdn as 1arctanax.](1)xe^x(2)xsinx(3)x^2lnx(4)xsin3x(5)xcos2x(6)xsec^2x(7)lnx(8)(lnx)^2(9)arctanxdn 相关知识点:
The following results illustrate the need of integration: 1. Trigonometric identity:cos2(x)=1+cos(2x)2. 2. Move the constant out:∫b⋅f(x)dx=b⋅∫f(x)dx. 3. Common integration:∫cos(u)du=sin(u). 4. The sum rule:∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx...
\int \cos(5x)-xe^{-2x} dx Use integration by parts. Integration by parts: use reduction formulas: \int of ,x^2cos,5x,dx Perform the integration: int 4 cos^3 x sin ^6 x dx a. {4}/{7}(sin^7x-sin^9x)+C b. {4}/{5}cos^5x-{4}/{7}cos^7x+C c. {4}/{5}sin...
sincos2cosxxdxxxxdx du=2xdxv=-cosx u=2x dv=cosxdx du=2dxv=sinx 22 sincos2sin2sinxxdxxxxxxdx 22 sincos2sin2cosxxdxxxxxxC 8.2TrigonometricIntegrals PowersofSineandCosine sincos nm uudusincoscossin nn uuduuudu22 sin1cosuu 1.Ifnisodd,leaveonesinufactoranduse forallotherfactorsofsin. ...
Chapter7 TechniquesofIntegration 7.1Integrationbyparts Question:Howtointegrate xlnxdx,xsinxdx,exsinxdx,wherethe integrandsaretheproductoftwokindsoffunctions?Everydifferentiationrulehasacorrespondingintegrationrule:Differentiation Integration theChainRuletheSubstitutionRule theProduct...
of the general form∫xmex dx •∫ 10xe3x dx •∫(x2 + 5)e-2xdx 1Math 152, c Benjamin Aurispa•∫x7e-x4dx Integrals of the general form∫xm cosx dx or∫xm sinx dx •∫3xsin 2x dx •∫x5 cos(x2) dx 2Math 152, c Benjamin AurispaIntegrals of the general form∫xm ...
Evaluate the integral \int_0^1\int_{\arcsin{y^{\pi/2}\cos{x}\sqrt{1 + \cos^2x}dxdy by reversing the order of integration. Evaluate the following integral by reversing the order of integration: \int_{-2}^{0} \int_{2}^{y^2} y^3 e^{x^3} dx dy Eval...
Chapter 7 Techniques of IntegrationLHospital Rule and Improper Integrals7.1 Basic Integration FormulasTable of Indefinite integrals xd) 1 ( C is a constant)Cxxxnd)2(Cxnn111xxd)3(Cx ln) 1(n)ln(xx121d)4(xxCx arctanxxdcos)6(Cx sinxx2cosd)8(xxdsec2Cx tanorCx cotarc21d)5(xxCx arcsin...
(Use C for the constant of integration.) \int x^{n} ln(ax)dx (a\neq0, n\neq-1) Use integration by parts to solve problem. \int x^{3}(\ln x) dx Use integration by parts to solve problem. \int e^{2x}(\sin x)...
Integration4.1 Indefinite Integrals Indefinite Integrals An indefinite integral of f(x) represent an entirely family of functions whose derivative is f(x) and is denoted bydxxf)()()(xFdxxfThen:means )()(xfxFExample 1:xxd34Cx313Because34)3(31xCxdxdExample 2:.dcossin22xxxxx dsin21Cx cos21...