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(25) xa+xdx= x(a+x) aln[ x+ x+a](26) x ax+b dx=215a2( 2b2+abx+ 3a2x2) ax+b(27) x(ax+b)dx=14a3/2[(2ax+b) ax(ax+b) b2ln a x+ a(ax+b) ](28) x3(ax+b)dx=[b12a b28a2x+x3] x3(ax+b)+b38a5/2ln a x+ a(ax+b) (29) x2 a2dx=12x x2 a2 12a2ln x+ x2 a2 3(30) a2 x2dx=

Table of Basic Integrals Basic Forms (1) Z xndx= 1 n+ 1 xn+1; n6= 1 (2) Z 1 x dx= lnjxj (3) Z udv= uv Z vdu (4) Z 1 ax+ b dx= 1 a lnjax+ bj Integrals of Rational Functions (5) Z 1 (x+ a)2 dx=

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