Question

Integrate the following
$\displaystyle{\bf{\rightarrow\;\;\green{\int \frac{ sinx + cosx}{ \sqrt{sin2x} }}.dx}}$
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Answer 1

Answer: Using integration by parts

∫sinhxdx=xcoshx−∫coshxdx=xcoshx−sinhx+constant

⇒∫xsinhx=xcoshx−∫coshxdx

⇒∫xsinhx=xcoshx−sinhx+constant

Answer 2

Step-by-step explanation:

∫ sin+cosx /√sin2x

Put sinx−cosx=t

(sinx+cosx)dx= dt

t^2 =1−sin2x

sin 2x = 1-t^2

∫ dt / √(1-t^2) =sin^-1 t+c

=sin^−1 (sinx−cosx)

=sin ^−1 {√2 sin(x−π/4)}

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