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
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