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b  [u(x) · v(x)] dx = [u(x) · v(x)] . 

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1 − x2 dx x2

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1 − sin t cos t dt = sin2 t

1 − sin2 t dt = sin2 t

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π/2 π π π π π − ctg t − t  = − ctg − + ctg + = 1 − . π/4 2 2 4 4 4

x2 ln x dx

5

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7'H"( u = ln x4 dv = x dx5 >! "( /+(' " 0+"+"& 1 #&( @.B6 2

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 e 1

cos2 t dt = sin2 t

e x3 2 x ln x dx = · ln x1 − 3

e 1

dx x3 du = v= x 3

L

e3 ln e ln 1 1 x3 1 · dx = − − 3 x 3 3 3

e3 1 3 e e3 = − x= − 3 9 1 3



e3 1 − 9 9

e

5 7+"( 

x2 dx =

1

1 2e3 1 = + = (1 + 2e3 ). 9 9 9





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