1. Standard Integral Forms These are the so
Transcription
1. Standard Integral Forms These are the so
1. Standard Integral Forms These are the so-called Standard Integral Forms, from Section 7.1. Z kdu = ku + C Z ur du = ur+1 /(r + 1) + C. Suppose r 6= −1. Then Z Suppose r = −1. Then Z Z ur du = ln(u) + C. eu du = eu + C au du = au /(ln(a)) if a > 0, a 6= 1 Z sin(u)du = −cos(u) + C Z cos(u)du = sin(u) + C Z sec2 (u)du = tan(u) + C Z csc2 (u)du = −cot(u) + C Z sec(u)tan(u)du = sec(u) + C Z csc(u)cot(u)du = −csc(u) + C Z tan(u)du = −ln|cos(u)| + C Z cot(u)du = ln|sin(u)| + C Z u du = sin−1 ( ) + C, for a > 0 2 a −u Z du 1 u = tan−1 ( ) + C, for a 6= 0 2 2 a +u a a Z √ a2 du 1 |u| √ = sec−1 ( ) + C, for a > 0 2 2 a a u u −a Z sinh(u)du = cosh(u) + C Z cosh(u)du = sinh(u) + C 1