Hi Split the sin8x dx into sin2x sin6 x dx, and mutiply the numerator and denominator by 3cosx, Hence the expression becomes 3sin2x sin6x cosx dx / 3cosx .. now take sin3x = t and substitute in the expression. We made this substitution because on differentiating sin3x , we get 3sin2x cosx dx, hence we can directly substitute it in the expresssion. After substitution we get, t2dt/3 (1-t2/3)1/2 . Again make a substitution of y2 = 1-t2/3 . Try at all times , to somehow eliminate the denominator term, wen u get to that step, use the formulas specified for particular forms.

Integral Calculus> integrate...

integrate sin^8x.dx

MD ASIF IQUBAL , 16 Years ago

Grade 12

2 Answers

AskiitianExpert Shine

Last Activity: 16 Years ago

Split the sin⁸x dx into sin²x sin⁶x dx, and mutiply the numerator and denominator by 3cosx,

Hence the expression becomes 3sin²x sin⁶x cosx dx / 3cosx .. now take sin³x = t and substitute in the expression. We made this substitution because on differentiating sin³x , we get 3sin²x cosx dx, hence we can directly substitute it in the expresssion.

After substitution we get, t²dt/3 (1-t^2/3)^1/2. Again make a substitution of y²= 1-t^2/3.

Try at all times , to somehow eliminate the denominator term, wen u get to that step, use the formulas specified for particular forms.

Nishavak

Last Activity: 8 Years ago

Use double angles.Calculative but easy sum.Just put sin^2(x) as (1-cos2x)/2. And go with the flow. You will reach ur answer pretty quick, provided you should have faster calculation speed.