Given that the indefinite integral
∫ sin 2 5 x cos 3 x d x
equals to
2 sin 2 A x [ B 1 − C 1 sin 2 x ]
neglecting the arbitrary constant.
Find the value of A + B − C .
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thanks a lot sir for posting it in Latex .
nice method...
How come level 5?
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please reduce it to level 3.
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Similar to Harshvardhan Mehta 's solution, but in LaTex here.
∫ sin 2 5 x cos 3 x d x = ∫ sin 2 5 x cos 2 x d sin x = ∫ sin 2 5 x ( 1 − sin 2 x ) d sin x = ∫ ( sin 2 5 x − sin 2 9 x ) d sin x = 7 2 sin 2 7 x − 1 1 2 sin 2 1 1 x = 2 sin 2 7 x [ 7 1 − 1 1 1 sin 2 x ]
⇒ A + B − C = 7 + 7 − 1 1 = 3