If the integral 5 tan x ? d x tan x - 2 = x + a l n | sin x - 2 cos x | + C then ' a ' is equal to (C is constant of integration)

Question

If the integral $\int \frac{5 \tan x d x}{\tan x - 2} = x + a l n$ $| \sin x - 2 \cos x |$ $+ C$ then $' a'$ is equal to (C is constant of integration)

Smart Achievers · Accepted Answer

(2)

$\int \frac{5 \sin x d x}{\sin x - 2 \cos x} = \int d x + 2 \int \frac{\cos x + 2 \sin x}{\sin x - 2 \cos x} d x = x + 2 \ln$ $| \sin x - 2 \cos x |$ $+ C$

Solution

Q.
If the integral $\int \frac{5 \tan x d x}{\tan x - 2} = x + a l n$ $| \sin x - 2 \cos x |$ $+ C$ then $' a'$ is equal to (C is constant of integration)

Ans.
(2)

$\int \frac{5 \sin x d x}{\sin x - 2 \cos x} = \int d x + 2 \int \frac{\cos x + 2 \sin x}{\sin x - 2 \cos x} d x = x + 2 \ln$ $| \sin x - 2 \cos x |$ $+ C$

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Solution

Q. If the integral ∫5tanx dxtanx-2=x+aln|sinx-2cosx|+C then 'a' is equal to (C is constant of integration)

Ans. (2) ∫5sinx dxsinx-2cosx=∫dx+2∫cosx+2sinxsinx-2cosxdx=x+2ln|sinx-2cosx|+C

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Q.
If the integral $\int \frac{5 \tan x d x}{\tan x - 2} = x + a l n$ $| \sin x - 2 \cos x |$ $+ C$ then $' a'$ is equal to (C is constant of integration)

Ans.
(2)

$\int \frac{5 \sin x d x}{\sin x - 2 \cos x} = \int d x + 2 \int \frac{\cos x + 2 \sin x}{\sin x - 2 \cos x} d x = x + 2 \ln$ $| \sin x - 2 \cos x |$ $+ C$