∫ 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 2 ( 1 + c o t A x ) B + C then AB= Options: A . &nbsp 1 B . &nbsp 2 C . &nbsp 1 2 D . &nbsp None of these

Answer: Option B : B I = ∫ c o s x 4 d x s i n 3 x ( s i n 5 x + c o s 5 x ) 3 5 = ∫ c o s e c 2 x c o t 4 x d x ( 1 + c o t 5 x ) 3 / 5 1 + c o t 5 x = t . 5 c o t 4 x ( − c o s e c 2 x ) d x = d t = − 1 5 ∫ d t t 3 / 5 = − t 2 / 5 2 = − 1 2 ( 1 + c o t 5 x ) 2 / 5 + C .

∫cos4xdxsin3x(sin5x+cos5x)35=−12(1+cotAx)B+C then AB=

Discussion Forum : Indefinite Integration

Question -

$\int \frac{c o s^{4} x d x}{s i n^{3} x (s i n^{5} x + c o s^{5} x)^{\frac{3}{5}}} = - \frac{1}{2} (1 + c o t^{A} x)^{B} + C$ then AB=

Options:

A . 1

B . 2

C .

\frac{1}{2}

D . None of these

Answer: Option B
:
B

I = \int \frac{c o s x^{4} d x}{s i n^{3} x (s i n^{5} x + c o s^{5} x)^{\frac{3}{5}}} = \int \frac{c o s e c^{2} x c o t^{4} x d x}{(1 + c o t^{5} x)^{3 / 5}} 1 + c o t^{5} x = t . 5 c o t^{4} x (- c o s e c^{2} x) d x = d t = \frac{- 1}{5} \int \frac{d t}{t^{3 / 5}} = \frac{- t^{2 / 5}}{2} = \frac{- 1}{2} (1 + c o t^{5} x)^{2 / 5} + C .

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Discussion Forum : Indefinite Integration

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