MIND FREK INTEGRAL(2)

$\int \sqrt 8 - s i n 2 x c o s x - s i n x d x$

ans-----> $s i n - 1 ( 3 s i n x + c o s x ) + c$

2 Answers

write sin2x as

$(s i n x + c o s x) 2 = 1 + s i n 2 x$

$s i n 2 x = (s i n x + c o s x) 2 - 1$

$\int \sqrt 8 - [(s i n x + c o s x) 2 - 1)] c o s x - s i n x $

$\int \sqrt 9 - (s i n x + c o s x) 2 c o s x - s i n x $

put sinx + cosx = t

cosx - sinx dx = dt

$\int \sqrt 9 - (t) 2 d t \to sin - 1 ( 3 t )$

got it simple it was.i had not tried it.[4][4]

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