integration substitution

substitution method for integration

Integration formulae

If an integral is not of a standard type, but can be reduced to a standard type by substitution

of the form
u = f(x)
du = f ' (x) dx take the differential on both sides if necessary

after substitution, remember that everything should be in terms of u alone

Examples on integration by substitution


* integral of x^3 / sqrt(9 - x^2)
answer and some explanation

* integral of (x^3)*sqrt[4-x^2]
answer and some explanation


* integral of 1 / { x*sqrt[ax-x^2]} using substitution
explanation of the answer to integration by substitution

*integral of 1 / 6{ [ x^(1/2)+ x^(1/3) ] } using substitution
answer with some explanation 


*integral of sqrt{[1-sqrt(x)] / [1+sqrt(x)]}
explanation and answer to the problem on integration

*integral of 2*cube of (tanx) with 0 to pi/4 as limits
explanation and answer to integral of 2*cube of (tanx) with 0 to pi/4 as limits




PAGE 1 BASIC INTEGRATION

PAGE 2 INTEGRATION BY SUBSTITUTION
 
PAGE 3 INTEGRATION BY COMPLETION OF SQUARES

PAGE 4 INTEGRATION BY PARTS

PAGE 5 INTEGRATION BY MANIPULATION OF NUMERATOR IN TERMS OF DENOMINATOR