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Integral Table

Table of Integrals Basic Forms xndx=1n+ 1xn+1(1) 1xdx= ln|x|(2) udv=uv vdu(3) 1ax+bdx=1aln|ax+b|(4)Integrals of Rational Functions 1(x+a)2dx= 1x+a(5) (x+a)ndx=(x+a)n+1n+ 1,n6= 1(6) x(x+a)ndx=(x+a)n+1((n+ 1)x a)(n+ 1)(n+ 2)(7) 11 +x2dx= tan 1x(8) 1a2+x2dx=1atan 1xa(9) xa2+x2dx=12ln|a2+x2|(10) x2a2+x2dx=x atan 1xa(11) x3a2+x2dx=12x2 12a2ln|a2+x2|(12) 1ax2+bx+cdx=2 4ac b2tan 12ax+b 4ac b2(13) 1(x+a)(x+b)dx=1b alna+xb+x, a6=b(14) x(x+a)2dx=aa+x+ ln|a+x|(15) xax2+bx+cdx=12aln|ax2+bx+c| ba 4ac b2tan 12ax+b 4ac b2(16)Integrals with Roots x adx=23(x a)3/2(17) 1 x adx= 2 x a(18) 1 a xdx= 2 a x(19) x x adx=23a(x a)3/2+25(x a)5/2(20) ax+bdx=(2b3a+2x3) ax+b(21) (ax+b)3/2dx=25a(ax+b)5/2(22) x x adx=23(x 2a) x a(23) xa xdx= x(a x) atan 1 x(a x)x a(24) xa+xdx=

Integrals with Trigonometric Functions Z sinaxdx= 1 a cosax (63) Z sin2 axdx= x 2 sin2ax 4a (64) Z sinn axdx= 1 a cosax 2F 1 1 2; 1 n 2; 3 2;cos2 ax (65) Z sin3 axdx= 3cosax 4a + cos3ax 12a (66) Z cosaxdx=

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