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(10)Zx a2+x2dx=1 2lnja2+x2j(11)Zx2 a2+x2dx=x�atan�1x a(12)Zx3 a2+x2dx=1 2x2�1 2a2lnja2+x2j(13)Z1 ax2+bx+cdx=2 p 4ac�b2tan�12ax+b p 4ac�b2(14)Z1 (x+a)(x+b)dx=1 b�alna+x b+x;a6=b(15)Zx (x+a)2dx=a a+x+lnja+xj(16)Zx ax2+bx+cdx=1 2alnjax2+bx+cj�b ap 4ac�b2tan�12ax+b p 4ac�b2IntegralswithRoots(17)Zp x�adx=2 3(x�a)3=2(18)Z1 p xadx=2p xa(19)Z1 p a�xdx=�2p a�x2 (30)Zp a2�x2dx=1 2xp a2�x2+1 2a2tan�1x p a2�x2(31)Zxp x2a2dx=1 3�x2a23=2(32)Z1 p x2a2dx=lnx+p x2a2(33)Z1 p a2�x2dx=sin�1x a(34)Zx p x2a2dx=p x2a2(35)Zx p a2�x2dx=�p a2�x2(36)Zx2 p x2a2dx=1 2xp x2a21 2a2lnx+p x2a2(37)Zp ax2+bx+cdx=b+2ax 4ap ax2+bx+c+4ac�b2 8a3=2ln2ax+b+2p a(ax2+bx+c)Zxp ax2+bx+cdx=1 48a5=22p ap ax2+bx+c��3b2+2abx+8a(c+ax2)+3(b3�4abc)lnb+2ax+2p ap ax2+bx+c(38)4 (48)Zln(ax+b)dx=x+b aln(ax+b)�x;a6=0(49)Zln(x2+a2)dx=xln(x2+a2)+2atan�1x a�2x(50)Zln(x2�a2)dx=xln(x2�a2)+alnx+a x�a�2x(51)Zln�ax2+bx+cdx=1 ap 4ac�b2tan�12ax+b p 4ac�b2�2x+b 2a+xln�ax2+bx+c(52)Zxln(ax+b)dx=bx 2a�1 4x2+1 2x2�b2 a2ln(ax+b)(53)Zxln�a2�b2x2dx=�1 2x2+1 2x2�a2 b2ln�a2�b2x2(54)Z(lnx)2dx=2x�2xlnx+x(lnx)2(55)Z(lnx)3dx=�6x+x(lnx)3�3x(lnx)2+6xlnx(56)Zx(lnx)2dx=x2 4+1 2x2(lnx)2�1 2x2lnx(57)Zx2(lnx)2dx=2x3 27+1 3x3(lnx)2�2 9x3lnx6 (68)Ze�ax2dx=p 2p aerf�xp a(69)Zxe�ax2dx=�1 2ae�ax2(70)Zx2e�ax2dx=1 4r a3erf(xp a)�x 2ae�ax2IntegralswithTrigonometricFunctions(71)Zsinaxdx=�1 acosax(72)Zsin2axdx=x 2�sin2ax 4a(73)Zsin3axdx=�3cosax 4a+cos3ax 12a(74)Zsinnaxdx=�1 acosax2F11 2;1�n 2;3 2;cos2ax(75)Zcosaxdx=1 asinax(76)Zcos2axdx=x 2+sin2ax 4a(77)Zcos3axdx=3sinax 4a+sin3ax 12a8 (78)Zcospaxdx=�1 a(1+p)cos1+pax2F11+p 2;1 2;3+p 2;cos2ax(79)Zcosxsinxdx=1 2sin2x+c1=�1 2cos2x+c2=�1 4cos2x+c3(80)Zcosaxsinbxdx=cos[(a�b)x] 2(a�b)�cos[(a+b)x] 2(a+b);a6=b(81)Zsin2axcosbxdx=�sin[(2a�b)x] 4(2a�b)+sinbx 2b�sin[(2a+b)x] 4(2a+b)(82)Zsin2xcosxdx=1 3sin3x(83)Zcos2axsinbxdx=cos[(2a�b)x] 4(2a�b)�cosbx 2b�cos[(2a+b)x] 4(2a+b)(84)Zcos2axsinaxdx=�1 3acos3ax(85)Zsin2axcos2bxdx=x 4�sin2ax 8a�sin[2(a�b)x] 16(a�b)+sin2bx 8b�sin[2(a+b)x] 16(a+b)(86)Zsin2axcos2axdx=x 8�sin4ax 32a(87)Ztanaxdx=�1 alncosax9 (98)Zcsc2axdx=�1 acotax(99)Zcsc3xdx=�1 2cotxcscx+1 2lnjcscx�cotxj(100)Zcscnxcotxdx=�1 ncscnx;n6=0(101)Zsecxcscxdx=lnjtanxjProductsofTrigonometricFunctionsandMono-mials(102)Zxcosxdx=cosx+xsinx(103)Zxcosaxdx=1 a2cosax+x asinax(104)Zx2cosxdx=2xcosx+�x2�2sinx(105)Zx2cosaxdx=2xcosax a2+a2x2�2 a3sinax(106)Zxncosxdx=�1 2(i)n+1[�(n+1;�ix)+(�1)n�(n+1;ix)]11 ProductsofTrigonometricFunctionsandEx-ponentials(117)Zexsinxdx=1 2ex(sinx�cosx)(118)Zebxsinaxdx=1 a2+b2ebx(bsinax�acosax)(119)Zexcosxdx=1 2ex(sinx+cosx)(120)Zebxcosaxdx=1 a2+b2ebx(asinax+bcosax)(121)Zxexsinxdx=1 2ex(cosx�xcosx+xsinx)(122)Zxexcosxdx=1 2ex(xcosx�sinx+xsinx)IntegralsofHyperbolicFunctions(123)Zcoshaxdx=1 asinhax(124)Zeaxcoshbxdx=8�&#x]TJ ;� -2;.52;&#x Td ;&#x[000;:eax a2�b2[acoshbx�bsinhbx]a6=be2ax 4a+x 2a=b(125)Zsinhaxdx=1 acoshax13