INTEGRATION_Trigonometric Functions and Hyperbolic Functions
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Course
MAT 2691
Institution
University Of South Africa
INTEGRATION: Trigonometric Functions & Hyperbolic Functions BACKGROUND THEORY Corresponding to each trigonometric (or hyperbolic) differentiation formula is an integration formula. Although these are always given in a formula sheet, it will help you a great deal in the exam in terms of saving time ...
BACKGROUND THEORY
Corresponding to each trigonometric (or hyperbolic) differentiation formula is an integration formula. Although these
are always given in a formula sheet, it will help you a great deal in the exam in terms of saving time if you learn the
formulas by heart.
Trigonometric Functions Hyperbolic Functions
d du d du
sin u cos u sinh u cosh u
dx dx dx dx
cos u du sin u C
cosh u du sinh u C
d du d du
cos u sin u cosh u sinh u
dx dx dx dx
sin u du cos u C
sinh u du cosh u C
d du d du
tan u sec2 u tanh u sech 2 u
dx dx dx dx
sec2 u du tan u C
sech 2 u du tanh u C
d du d du
sec u sec u tan u sech u sech u tanh u
dx dx dx dx
sec u tan u du sec u C
sech u tanh u du sech u C
d du d du
csc u csc u cot u csch u csch u coth u
dx dx dx dx
csc u cot u du csc u C
csch u coth u du csch u C
d du d du
cot u csc2 u coth u csch 2 u
dx dx dx dx
csc2 u du cot u C
csch 2 u du coth u C
Special Standard Integrals:
Trigonometric Functions Hyperbolic Functions
tan udu ln sec u C tanh u du ln cosh u C
cot u du ln sin u C coth u du ln sinh u C
sec u du ln sec u tan u C sech u du arctan sinh u C
csc u du ln csc u cot u C csch u du ln tanh C u
2
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