Найти указанные неопределенные интегралы и результаты проверить дифференцированием

Проверка:
(13arcsinx3+C)'=ddx(x)+13(ddx(arcsinx3))=13(ddx(arcsinx3))+0=
=13ddxarcsinx3=13*ddxx31-x6=3x2*121-x6=x21-x6
б) Подробное разложение подынтегральной функции:
x3+2x2+2x+1
x-2+3x+4x2+2x+1
3x+4x2+2x+1=3x+4(x+1)2
3x+4(x+1)2=ax+1+b(x+1)2
3x+4=ax+1+b
3x+4=a+xa+b
4=a+b
3=a
1110ab=43
111043
110-14-1
110141
100131
a=3
b=1
3x+4x2+2x+1=3x+1+1(x+1)2
x3+2(x+1)2=x+3x+1+1(x+1)2-2
x3+2x2+2x+1dx=x3+2(x+1)2dx=(x+3x+1+1(x+1)2-2)dx=31x+1dx+
+1(x+1)2dx+xdx-2*1dx=31udu+1(x+1)2dx+xdx-
-2*1dx=3Inu+1x+12dx+xdx-2*1dx=3Inu+
+1s2ds+xdx-2*1dx=-1s+3Inu+xdx-2*1dx=
=-1s+x22+3Inu-2*1dx=-1s+3Inu+x22-2x+C=
=3Inu+x22-2x-1x+1+C=x22-2x+3Inx+1+C=
=x3-3x2-4x+6x+1Inx+1-22(x+1)+C=
=12x2-4x-2x+1+6Inx+1-5+C
Проверка:
12x2-4x-2x+1+6Inx+1-5+C'=ddxC+12(ddx(-5-4x+
+x2-2x+1+6In(1+x)))=12(ddx(-5-4x+x2-2x+1+6In(1+x)))+
+0=12ddx-5-4x+x2-2x+1+6In1+x=12ddx-5-
-4ddxx+ddxx2-2ddx1x+1+6ddxIn1+x=
=12-4ddxx+ddxx2-2ddx1x+1+6ddxIn1+x+0=
=12-4ddxx+ddxx2-2ddx1x+1+6ddxIn1+x=
=12ddxx2-2ddx1x+1+6ddxIn1+x-1*4=
=12-4-2ddx1x+1+6ddxIn1+x+2x=
=12-4+2x+6ddxIn1+x-2-ddx1+x1+x2=
=12-4+2x+2ddx1+x1+x2+6ddxIn1+x=
=12(-4+2x+6ddxIn1+x+ddx1+ddxx21+x2=
=12-4+2x+6ddxIn1+x+2ddxx+01+x2=
=12-4+2x+2ddxx1+x2+6ddxIn1+x=
=12-4+2x+6ddxIn1+x+1*21+x2=
=12-4+2x+21+x2+6ddx1+x1+x=12(-4+2x+21+x2+
+ddx1+ddxx61+x)=12-4+2x+21+x2+6ddxx+01+x=
=12-4+2x+21+x2+6ddxx1+x=12(-4+2x+21+x2+1*
*61+x=2+x3(1+x)2
в) xcos3xdx=13xsin3x-13sin3xdx=13xsin3x-19sinudu=
=cos⁡(u)9+13xsin3x+C=13xsin3x+19cos*3x)+C=19(3xsin(3x)+
+cos⁡(3x))+C
Проверка:
193xsin3x+cos3x+C'=ddxC+19(cos3x+3xsin3x))=
=19ddxcos3x+3xsin3x+0=19ddxcos3x+3xsin3x=
=19ddxcos3x+3ddxxsin3x=19(3ddxxsin3x+
+-ddx3xsin3x)=19(3ddxxsin3x-3ddxxsin3x=
=19-3ddxxsin3x+3xddxsin3x+ddxxsin3x=
=19-3ddxxsin3x+3ddxxsin3x+cos3xddx3xx=
=193xcos3xddx3x+ddxxsin3x-1*3sin3x=
=19-3sin3x+3ddxxsin3x+3ddxxxcos3x=
=19-3sin3x+3ddxxsin3x+1*3xcos3x=
=19-3sin3x+33xcos3x+1*sin3x=xcos(3x)