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The value of 2intsinx.cosec 4x dx is eq...

The value of `2intsinx.`cosec` 4x` dx is equal to

A

`1/(2sqrt(2))"ln"|(1+sqrt(2)sinx)/(1-sqrt(2)sinx)|-1/4"ln"|(1+sinx)/(1-sinx)|+C`

B

`1/(2sqrt(2))"ln|(1+sqrt(2)sinx)/(1-sqrt(2)sinx)-1/2"ln"|(1+sinx)/(cosx)|+C`

C

`1/(2sqrt(2))"ln"|(1-sqrt(2)sinx)/(1+sqrt(2)sinx)|-1/4"ln"|(1+sinx)/(1-sinx)|+C`

D

`-1/(2sqrt(2))"ln"|(1-sqrt(2)sinx)/(1+sqrt(2)sinx)|+1/4"ln"|(1-sinx)/(1+sinx)|+C`

Text Solution

AI Generated Solution

To solve the integral \( 2 \int \sin x \cos 4x \, dx \), we can follow these steps: ### Step 1: Rewrite the Integral We start with the integral: \[ I = 2 \int \sin x \cos 4x \, dx \] ...
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