^2x( x+ x)^2dx=

Question

^2x( x+ x)^2dx=

Accepted Answer

Correct answer: B. (b) sec^2 ⁡ xdx ( sec ⁡x+ tan ⁡x )^2 Let sec ⁡x+ tan ⁡x=t and sec ⁡x- tan ⁡x= 1t ⇒2 sec ⁡x=(t+ 1t) also( sec ⁡ xtan ⁡x+ sec^2 ⁡x) dx= dt sec ⁡x ( sec ⁡x+ tan ⁡x ) dx= dt t sec ⁡ xdx= dt ⇒ 12(t+ 1t) dttt^2= 12 ( 1+ 1t^2t^2 ) dt= 12 ( (t^-2+t^-4) dt )= 12( -1t- 13t^3)+C= 12 ( -3t^2-13t^3 )+C= -1-3 ( sec ⁡x+ tan ⁡x )^36 ( sec ⁡x+ tan ⁡x )^3+C .

$\int \frac{s e c ^{2} x}{( s e c x + t a n x ) ^{2}} d x =$

Solution

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