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What is the i...

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What is the integration of 1/kx dx ?

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Q. Integration of

\int \frac{1 + cos 4 x}{cot x - tan x} d x

- \frac{1}{8} cos k x

\int \frac{1 - {(cot x)}^{2008}}{tan x + {(cot x)}^{2009}} d x = \frac{1}{k} ln ∣ ∣ {sin}^{k} x + {cos}^{k} x ∣ ∣ + C

for arbitrary constant of integration

C,

then the value of

k

\int \frac{x e^{x} d x}{(x + 1)^{2}}

equal to?
where

c

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Q. For what values of

p

, is the integral

\int_{1}^{\infty} \frac{d x}{x^{p}}

Q. The value of the integral

\int_{0}^{π} \frac{sin k x}{sin x} d x

(k

is an even integer) is equal to

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