INTEGRATION

âˆ« 1âˆš3 sin x + cos x dx

(there is no square root on sinx it's just âˆš3 sin x is outside root.)

[ ans - 12 log l tan (x2 + pi12) + c ]

2 Answers

√√3 sinx + cosx

acosx + bsinx form where b = √3

a= 1

c= √a^2 + b^2 = √3+ 1
= 2

write it as
acosxc+ bsinx c

â†’ cosx2 +√3sinx 2

use cos ( a + b ) or sin ( a + b ) form and then integrate

short cut is

\int \frac{dx}{a sin x + bcosx } = \frac{1}{\sqrt{a^2 + b^2}} log \left\left|tan\left(\frac{x}{2}+ \frac{\tan^{-1} \frac{b}{a}}{2} \right) \right|+ c

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