Advertisements
Advertisements
Question
\[\int\frac{\cos 2x - 1}{\cos 2x + 1} dx =\]
Options
tan x − x + C
x + tan x + C
x − tan x + C
− x − cot x + C
MCQ
Solution
x − tan x + C
\[\int\left( \frac{\cos 2x - 1}{\cos 2x + 1} \right)dx\]
\[ = \int\left( \frac{1 - 2 \sin^2 x - 1}{2 \cos^2 x - 1 + 1} \right)dx\]
\[ = - \int \tan^2 x dx\]
\[ = - \int\left( \sec^2 x - 1 \right)dx\]
\[ = \int\left( 1 - \sec^2 x \right)dx\]
\[ = x - \tan x + C\]
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
\[\int\left( \frac{m}{x} + \frac{x}{m} + m^x + x^m + mx \right) dx\]
\[\int\frac{\cos^2 x - \sin^2 x}{\sqrt{1} + \cos 4x} dx\]
If f' (x) = a sin x + b cos x and f' (0) = 4, f(0) = 3, f
\[\left( \frac{\pi}{2} \right)\] = 5, find f(x)
\[\int\frac{1 - \cos x}{1 + \cos x} dx\]
` ∫ 1/ {1+ cos 3x} ` dx
Integrate the following integrals:
\[\int\text { sin x cos 2x sin 3x dx}\]
\[\int\left( \frac{x + 1}{x} \right) \left( x + \log x \right)^2 dx\]
` ∫ x {tan^{- 1} x^2}/{1 + x^4} dx`
\[\int\frac{1}{\left( x + 1 \right)\left( x^2 + 2x + 2 \right)} dx\]
` ∫ tan^3 x sec^2 x dx `
\[\int \sin^3 x \cos^5 x \text{ dx }\]
\[\int\frac{x}{x^4 + 2 x^2 + 3} dx\]
\[\int\frac{1}{\sqrt{7 - 6x - x^2}} dx\]
` ∫ {x-3} /{ x^2 + 2x - 4 } dx `
`int 1/(cos x - sin x)dx`
\[\int\frac{1}{p + q \tan x} \text{ dx }\]
\[\int\text{ log }\left( x + 1 \right) \text{ dx }\]
\[\int x^2 \sin^{- 1} x\ dx\]
\[\int x \sin^3 x\ dx\]
\[\int \cos^3 \sqrt{x}\ dx\]
\[\int\frac{x^2 \sin^{- 1} x}{\left( 1 - x^2 \right)^{3/2}} \text{ dx }\]
\[\int e^x \left( \frac{\sin 4x - 4}{1 - \cos 4x} \right) dx\]
\[\int e^x \frac{\left( 1 - x \right)^2}{\left( 1 + x^2 \right)^2} \text{ dx }\]
\[\int e^x \left( \log x + \frac{1}{x} \right) dx\]
\[\int e^x \left( \log x + \frac{1}{x^2} \right) dx\]
\[\int\left( x + 2 \right) \sqrt{x^2 + x + 1} \text{ dx }\]
\[\int\frac{x^2 + 1}{\left( 2x + 1 \right) \left( x^2 - 1 \right)} dx\]
\[\int\frac{x}{\left( x - 3 \right) \sqrt{x + 1}} dx\]
\[\int\frac{1}{\left( x^2 + 1 \right) \sqrt{x}} \text{ dx }\]
\[\int\frac{1}{7 + 5 \cos x} dx =\]
\[\int\frac{\sin x + \cos x}{\sqrt{\sin 2x}} \text{ dx}\]
\[\int\frac{1}{x^2 + 4x - 5} \text{ dx }\]
\[\int\frac{1}{4 \sin^2 x + 4 \sin x \cos x + 5 \cos^2 x} \text{ dx }\]
\[\int\frac{1}{\sin^2 x + \sin 2x} \text{ dx }\]
\[\int {cosec}^4 2x\ dx\]
\[\int\frac{6x + 5}{\sqrt{6 + x - 2 x^2}} \text{ dx}\]
\[\int \tan^3 x\ \sec^4 x\ dx\]
\[\int x\sqrt{1 + x - x^2}\text{ dx }\]
\[\int \left( \sin^{- 1} x \right)^3 dx\]
\[\int\frac{x \sin^{- 1} x}{\left( 1 - x^2 \right)^{3/2}} \text{ dx}\]
