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

integral of 2* (tanx)^3 with 0 to pi/4 as limits

write (tanx)^3 as the product of tanx and (tanx)^2

use  trigonometric formulae to rewrite  (tanx)^2 as [ (secx)^2 -1]

multiply the  tanx into [ (secx)^2 -1] and split into two integrals

for the first one, use the substitution t =tanx

the second integral is a direct formula.

formulae on integration
 
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


PAGE 6 INTEGRATION USING PARTIAL FRACTIONS

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