Table of Basic Integrals Basic Forms

Table of Basic IntegralsBasic Forms (1) xndx=1n+ 1xn+1, n6= 1(2) 1xdx= ln|x|(3) udv=uv vdu(4) 1ax+bdx=1aln|ax+b| Integrals of Rational Functions(5) 1(x+a)2dx= 1x+a(6) (x+a)ndx=(x+a)n+1n+ 1,n6= 1(7) x(x+a)ndx=(x+a)n+1((n+ 1)x a)(n+ 1)(n+ 2)(8) 11 +x2dx= tan 1x(9) 1a2+x2dx=1atan 1xa1(10) xa2+x2dx=12ln|a2+x2|(11) x2a2+x2dx=x atan 1xa(12) x3a2+x2dx=12x2 12a2ln|a2+x2|(13) 1ax2+bx+cdx=2 4ac b2tan 12ax+b 4ac b2(14) 1(x+a)(x+b)dx=1b alna+xb+x, a6=b(15) x(x+a)2dx=aa+x+ ln|a+x|(16) xax2+bx+cdx=12aln|ax2+bx+c| ba 4ac b2tan 12ax+b 4ac b2 Integrals with Roots(17) x a dx=23(x a)3/2(18) 1 x adx= 2 x a(19) 1 a xdx= 2 a x2(20) x x a dx= 2a3(x a)3/2+25(x a)5/2,or23x(x a)3/2 415(x a)5/2,or215(2a+ 3x)(x a)3/2(21) ax+b dx=(2b3a+2x3) ax+b(22) (ax+b)3/2dx=25a(ax+b)5/2(23) x x adx=23(x 2a) x a(24) xa xdx= x(a x) atan 1 x(a x)x a

e ax2 dx= p ˇ 2 p a erf x p a (69) Z xe ax2 dx= 1 2a e 2 (70) Z x2e ax2 dx= 1 4 r ˇ a3 erf(x p a) x 2a e ax2 Integrals with Trigonometric Functions (71) Z sinaxdx= 1 a cosax (72) Z sin2 axdx= x 2 sin2ax 4a (73) Z sin3 axdx= 3cosax 4a + cos3ax 12a (74) Z sinn axdx= 1 a cosax 2F 1 1 2; 1 n 2; 3 2;cos2 ax (75) Z cosaxdx= 1 a sinax (76) Z cos2 ...

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