Substitution involving Trigonometric Integrals
Substitution involving Trigonometric Integrals:
In solving trigonometric integrals, it would be beneficial to know a good amount of trig. identities to help simplify an integral.
ex.
Calculus
Forum reference:
Book page:
http://course-notes.org/Calculus
Substitution
Substitution:
The u substitution:
ex.
ò 2x(x2 + 3)2 dx
Integral of a Cosecant
Integral of a Cosecant:
ò csc u · u' dx = ln |csc u - cot u | + C
Integral of a Secant
Integral of a Secant:
ò sec u · u' dx = ln |cos u + tan u | + C
Integral of a Cotangent
Integral of a Cotangent:
ò cot u · u' dx = ln |sin u | + C
Integral of a Tangent
Integral of a Tangent:
ò tan u · u' dx = -ln |cos u| + C
Inverse Hyperbolic Functions
Inverse Hyperbolic Functions
Integral Of Inv. Hyperbolic Functions:
du = u' dx;
Hyperbolic Functions
Hyperbolic Functions
Many identities of hyp. functions are quite similar to corresponding trig. function identities.
Integrals of Hyperbolic Functions:
If u is a function x, where u' dx = du, then
Exponentials and Logarithms
Exponentials and Logarithms:
Integrals Involving Logarithms and Exponentials:
Inverse Trigonometric Functions
Inverse Trigonometric Functions:
Integral of Inverse Trig. Functions:
Let u be a function of x:Â
 
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