I=∫sec2x(secx+tanx)9/2dx, we will use the substitution t=secx+tanx. Step 1: Substitute t=secx+tanx From the identity sec2x=1+tan2x and the derivative of t: dtdx=secxtanx+sec2x=sec2x+secxtanx. Thus, we can express dx in terms of dt: dx=dtsec2x+secxtanx. Step 2: Rewrite se...
∫ sec2x dx = tanx+C ∫ cosec2x dx = -cotx+C ∫ sec2x dx = tanx+C ∫ secx tanxdx = secx+C ∫ cscx cotx dx = -cscx+C ∫1/(√(1-x2))= sin-1 x + C ∫-1/(√(1-x2))= cos-1 x + C ∫1/(1+x2)= tan-1 x + C ∫-1/(1+x2)= cot-1 x + C ∫1/(x...
∫03πsecx9dx. Integration by Substitution Method: In calculus, the substitution method is helpful in integrating a composite function. A composite is formed by two functions; thus, it is hard to integrate it. So that, a variableuis replaced with a function among those functions, and we inte...
Homework Statement Evaluate the definite (from -0.3 to 0.3) integral ∫tanxdx Homework Equations (dy/dx)tanx=(secx)^2 The Attempt at a Solution Using...
常用积分表（Common integral table）Common integral formula (a) containing the integral (axb+0a =) Formula 1.dxaxb+ = 1lnaxbCa++ 2. = (axbx) + 11 (formula)(1)AxbCa + + + Mu + (U = 1.)3.dxxaxb+ = formula 21 (LN) axbbaxbCa+.++ The 4.2dxxaxb+ formula (2) = 22311 (...
(0) 2arctan(0) AxbbCbbaxbbaxbCbbb.+. +>. ++.. 1 +<... 16.2dxxaxb+=formula D2axbaxbxbxaxb+ . +formula 17.daxbxx+=formula D2xaxbbxaxb++ +formula 18.2daxbxx+=formula D2axbaxxxaxb+ 1 +formula (three)anintegralcontaining2xa+ 19.22dxxa+formula=1arctanxCaa+ 20.22d(nxxa+)for...