Integrate the following :
(1) x e-x Solution
(2) x cos x Solution
(3) x cosec2x Solution
(4) x sec x tan x dx Solution
(5) 2 x e3x Solution
(6) x2 e 2x Solution
(7) x5 e^x2 Solution
(8) x tan2 x Solution
(9) x cos2 x Solution
(10) x cos 5 x cos 2 x Solution
(11) x2 cos 3x Solution
(12) cosec3x Solution
(13) eax cos bx Solution
(14) tan-1 x Solution
(15) (sin-1x) (e^sin-1x)/√(1 - x²) Solution
(16) tan-1 [(3x-x3)/(1-3x2)] Solution
(17) x sin-1 (x2) Solution
Answers :
(1) -e-x (x + 1) + C
(2) x sin x + cos x + C
(3) -x cot x + log (sin x) + C
(4) x sec x - log (sec x + tan x) + C
(5) (2/3) e3x [x - (1/3)] + C
(6) (1/2) (e2x)[x - (1/2)] + C
(7) (1/2)e^x2 [x4- 2 x2+ 2]+ C
(8) x (tan x) - log (cos x) - (x2/2) + C
(9) (1/2) [(x²/2)+ (x/2) (sin 2 x) + (1/4) (cos 2x) + C
(10) (1/2){(x/7)(sin 7x) + (1/49) (cos 7x)+(x/3)(sin 3x)+(1/9)(cos 3x)}+ C
(11) (x2/3)sin 3x + (2/9)[x cos 3 x] - (2/27)[sin 3x] + C
(12) (1/2)[-cosec x cot x] + (1/2)[log tan (x/2)] + C
(13) [eax/(a²+b²)][a cos b x + b sin bx]
(14) x tan-1 x- (1/2) log (1+x2) + C
(15) e^sin-1x (sin-1x - 1) + C
(16) 3xtan-1x - (3/2) log (1+x2) + C
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