Integrate by parts: \int ^{.02} _0 xe ^{-2x} dx Integrate by Parts \int x(5x+1)^{19}dx Integrate the following using integration by parts. \int (\tan x)^5(\sec x)^2\ dx Solve using integration by parts. \int x^2(\ln x)^2 dx ...
\int\sec^nx\;dx=\frac{\tan x \sec^{n-2}x}{n-1}+\frac{n-2}{n-1}\int\sec^{n-2}x\;dx\quad (n\neq 1) Use integration by parts to prove the reduction formula. \int \tan^n x\; dx = \frac{\tan^{n-1}x}{n-1}-\int \tan^{n-2}x\...
题目【题目】Use integration by parts to find the integral of the following functions with respect tox:Hint: In (7) write n as 1nz.In (9) write arctanz as 1arctan.(1)2(2) xsinx(3) x^2lnx(4)z sin3(5 xcos2x(6) xsec^2x(7)n(8) (lnx)^2(9)arctan z 相关知识点: ...
Chapter7 TechniquesofIntegration 7.1Integrationbyparts Question:Howtointegrate xlnxdx,xsinxdx,exsinxdx,wherethe integrandsaretheproductoftwokindsoffunctions?Everydifferentiationrulehasacorrespondingintegrationrule:Differentiation Integration theChainRuletheSubstitutionRule theProduct...
5、sinxdxdx(9)sincosxdxdx 2(10)sectanxdxdx2(11) csccotxdxdx 21(12)arcsin1dxdxx21(14)arctan1dxdxx21(13)arccos1dxdxx 21(15)arccot1dxdxx The Substitution Rulecxcuududxxxdxxu2sin21sin21cos2122cos212cos2xu2Example:Letthendxdu2ceceduedxxedxxexuuxuxx2222212121)2(212xu Letthenxdxdu2 The ...
\int x \:ln\: 2x\:dx Integrate using integration by parts \int \sin(2x)\sin(2x)dx Find the indefinite integral. Use C for the constant of integration. a) \int tan (7\theta) d \theta b) \int cos (\frac{t}{3}) ...