Table of Basic Integrals Basic Forms ∫xndx=1n+1xn+1,n≠−1 ∫xndx=1n+1xn+1,n≠−1 (1) ∫1xdx=ln∣∣∣x∣∣∣ ∫1xdx=ln|x| (2) ∫udv=uv−∫vdu ∫udv=uv−∫vdu (3) ∫1ax+bdx=1aln∣∣∣ax+b∣∣∣ ∫1ax+bdx=1aln|ax+b| (4) Integrals of Rational Functions ∫1(x+a)2dx=−1x+a ∫1(x+a)2dx=−1x+a (5) ∫(x+a)ndx=(x+a)n+1n+1,n≠−1 ∫(x+a)ndx=(x+a)n+1n+1,n≠−1 (6) ∫x(x+a)ndx=(x+a)n+1((n+1)x−a)(n+1)(n+2) ∫x(x+a)ndx=(x+a)n+1((n+1)x−a)(n+1)(n+2) (7) ∫11+x2dx=tan−1x ∫11+x2dx=tan−1x (8) ∫1a2+x2dx=1atan−1xa ∫1a2+x2dx=1atan−1xa (9) ∫xa2+x2dx=12ln∣∣∣a2+x2∣∣∣ ∫xa2+x2dx=12ln|a2+x2| (10) ∫x2a2+x2dx=x−atan−1xa ∫x2a2+x2dx=x−atan−1xa (11) ∫x3a2+x2dx=12x2−12a2ln∣∣∣a2+x2∣∣∣ ∫x3a2+x2dx=12x2−12a2ln|a2+x2| (12) ∫1ax2+bx+cdx=24ac−b2−−−−−−−√tan−12ax+b4ac−b2−−−−−−−√ ∫1ax2+bx+cdx=24ac−b2tan−12ax+b4ac−b2 (13) ∫1(x+a)(x+b)dx=1b−alna+xb+x, a≠b ∫1(x+a)(x+b)dx=1b−alna+xb+x, a≠b (14) ∫x(x+a)2dx=aa+x+ln∣∣∣a+x∣∣∣ ∫x(x+a)2dx=aa+x+ln|a+x| (15) ∫xax2+bx+cdx=12aln∣∣∣ax2+bx+c∣∣∣−ba4ac−b2−−−−−−−√tan−12ax+b4ac−b2−−−−−−−√...
