Конспект лекций по математическому анализу. Шерстнев А.Н. - 77 стр.

Z                             n+1                 Z
    (x , a)ndx = (x n,+a)1          + C (n 6= ,1); cos xdx = sin x + C ;
Z                                                 Z
     dx
    x , a = ln jx , aj + C ;                          sin xdx = , cos x + C ;
Z                                                 Z
    axdx =      1 x                                   dx2 = tg x + C ;
               ln a a + C ;                         cos x
Z                                                 Z
                                                      dx
    exdx = ex + C ;                                 sin2 x = , ctg x + C ;
Z                                                 Z
  p 2dx 2 = arcsin xa + C (a > 0);                   dx             x
                                                    sin x = ln j tg 2 j + C ;
   a ,x
Z                                               Z
  p 2dx 2 = ln x + pa2 + x2 + C ;                   sh xdx = ch x + C ;
    a +x
Z                                                 Z
    dx      1       x
  a2 + x2 = a arctg a + C (a 6= 0);                 ch xdx = sh x + C .

          Z
     8.         2
                   dx m (
 = p2 , 4q < 0; m 2 N). pODSTANOWKOJ t = x + p=2
              (x + px + q)
\TOT INTEGRAL Z SWODITSQ K P. 7.
                     dx
                x2 + px + q (
 = p , 4q > 0). iMEEM x + px + q =
   9. J =                           2                      2
(x , 1)(x , 2); 1 =   6 2, I
                    Z 1          1  dx = 1 ln j x , 1 j + C:
     J = ,1                   ,
                        x, 1 x, 2
            1     2                           1, 2 x, 2
       Z ( x + )dx         Z (2x + p)dx    2        Z
   10.
          x2 + px + q = 2 x2 + px + q + 2       , p 
 x2 +dx px + q
                                Z
 = 2 ln jx2 + px + qj + , 2p 
 x2 +dx   px + q ( =6 0).
       Z ( x + )dx
   11.
          (x2 + px + q)m (m > 1; 
 < 0). pRIEMOM P. 10 SWODITSQ K P. 7.

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