## Vineet Loomba is teaching live on Unacademy Plus

INDEFINITE INTEGRATION INTEGRATION BY PARTS IIT-IEE MATHS MADE EASY PREPARED BY: ER. VINEET LOOMBA IITiAN | IIT-JEE MENTOR FoR SURE SHoT SUcCESS IN JEE MAIN AND ADVANCED (IIT-JEE)

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) ABOUT ME B.Tech. From IIT Roorkee IIT-JEE Mentor Since 2010 Doubts/Feedback in Comment Section * Comment other topics you want to revise. Follow me @ https://unacademy.com/user/vineetloomba to get updates or search me on Google * Share among your peers as SHARING is CARING!!

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Integration By Parts du dx where u & v are differentiable functions and are commonly designated as first & second function respectively. product of two functions - (first function) x (integral of the second function) Integral of [(differential coefficient of the first function) The integral of the x (integral of the second function)]" MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) ILATE Rule Choose the first function as the function which comes first in the word ILATE, where; IInverse function, L-Logarithmic function, A-Algebraic function, T-Trigonometric function & E-Exponential function. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Illustration: Evaluate:x2 sin x dx Solution: x2 sin x dx = x | sin x dx-1 (2x | sin x dx)dx -x' cos x +2[x scos x dx -ascos x dx)dx =-x-cos x + 2x sin x-2 cos x + c MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) X sin 'X dx Example Find J Solution Let fint function be sin 'x and second function be a Frst we find the integral of the second f nction,ie. x dr First we find the integral of the second function, i.e. Put t=1-x". Then dt =-2xdx x dx Therefore x sin"xdx = (sin-ix)-1-X2 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Illustration: Evaluate: (cos#xdx Solution Consider I-cos Vxdx Let then- Vx dx = 2Vxdt Icost.2tdt i.e. or dx = 2t dt SO taking t as first function, then integrate it by part 1-2 | t cos tdt cos tdt dt = 2| tsin t- 1.sin tdt l = 2[tsin t-cost]-c MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Illustration Evaluate : Jit sinx dx x(1-sinx) (1 +sinx)(1 -sin x) dxx sec xdx x sec x tan xdx Solution: Let I= dx dx 1 sin x x(1 sin x) x(1 -sinx) | 1-sin#x coS X x sec xdx - sec xdx dx x secx tan xdx- sec x tan xdx dx tan xdx-xsecx secxdx = [xtan x-enl sec x1]-[xsec x-In l sec x + tan x 1]-c x (tan x - sec x) +secx + tanx)X(1-sin x) -x 1 - sinx) = x ( tan x-sec x) + In + En 1 sin x | +c sec x coS X MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) ENROL for this Course (Free) Enroll 439 Recommend Lessons (Like) E . Rate and Review the Course .Comments . Sharing with friends 15 68 26 ratings 7 reviews Share MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)