If ∫ c o s 4 x d x s i n 3 x s i n 5 x + c o s 5 x 3 5 = - 1 K 1 + c o t P x K P + C , then the value of K + P is equal to (where C is the constant of integration)

Question

If ∫ c o s 4 x d x s i n 3 x s i n 5 x + c o s 5 x 3 5 = - 1 K 1 + c o t P x K P + C , then the value of K + P is equal to (where C is the constant of integration),

MARKS App · Accepted Answer

Let, I = ∫ c o s 4 x d x s i n 6 x 1 + c ot 5 x 3 5 = ∫ s e c 2 x d x t a n 6 x 1 + 1 t a n x 5 3 5 Substituting, 1 + 1 tan ⁡ x 5 = t and - 5 tan 6 ⁡ x sec 2 ⁡ x d x = d t I = - 1 5 ∫ d t t 3 / 5 = - 1 5 t 2 5 2 5 + C = - 1 2 ∫ 1 + c o t 5 x 2 5 + C Hence, K = 2 , P = 5

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