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pink_ele

INTEGRALS

Well dear !

I really find dese sometimes really confusing , when not learnt proper ly soooooooooooooo posting it here

In e^ax sinbx dx =e^ax/a²+b² (a sinbx +b cosbx)

In sin mx cos nx dx

(i)If one of dem is odd den subs for odd one (i.e put it equal to t )

(ii)If both r odd then then subs for anyone

And

(iii)If both r even

Den simple trigo will work

Well

If m, n r just rational

Then

(a)Look, if (m+n-2)/2 is an integer

Further this will be so if m+n is even (for eg 3/2 and 1 /2 )

Then put cot x or tan x =variable say p

Whatever u find convenient dear

For integrela of d form

x^m (a+bxⁿ)^Pdx

(i)If p is an positive integer then do simple expansionJ

(ii)If p is negative integer then

Put x=t^k

Where k is L.C.M of m,n

(iii)And if p is a fraction

Then there r 2 cases

(a) If (m+1)/n is an integer

Then (a+bxⁿ)= t^k

Where k is dr of p

(b)Nd if

((m+1)/n)+P is an integer den (here p is a fraction )

Put (a+bxⁿ) = t^k xⁿ

^{hope it helped}