Advertisements
Advertisements
Question
\[\int\frac{\cos x}{\sqrt{4 + \sin^2 x}} dx\]
Sum
Advertisements
Solution
` ∫ { cos x dx}/{\sqrt{4 + sin^2 x}} `
\[\text{ let }\sin x = t\]
\[ \Rightarrow \text{ cos x dx }= dt\]
Now, ` ∫ { cos x dx}/{\sqrt{4 + sin^2 x}} `
\[ = \int\frac{dt}{\sqrt{2^2 + t^2}}\]
\[ = \text{ log } \left| t + \sqrt{4 + t^2} \right| + C\]
\[ = \text{ log } \left| \sin x + \sqrt{4 + \sin^2 x} \right| + C\]
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
\[\int\left( \frac{m}{x} + \frac{x}{m} + m^x + x^m + mx \right) dx\]
\[\int\frac{\cos x}{1 + \cos x} dx\]
\[\int\frac{1 + \cos x}{1 - \cos x} dx\]
\[\int\frac{1 - \cos x}{1 + \cos x} dx\]
\[\int\frac{1}{\text{cos}^2\text{ x }\left( 1 - \text{tan x} \right)^2} dx\]
\[\int\frac{2x + 1}{\sqrt{3x + 2}} dx\]
\[\int\left( 5x + 3 \right) \sqrt{2x - 1} dx\]
\[\int \text{sin}^2 \left( 2x + 5 \right) \text{dx}\]
\[\int \sin^2 \frac{x}{2} dx\]
` ∫ sin 4x cos 7x dx `
Integrate the following integrals:
\[\int\text{sin 2x sin 4x sin 6x dx} \]
\[\int\frac{1 - \cot x}{1 + \cot x} dx\]
` ∫ {"cosec" x }/ { log tan x/2 ` dx
\[\int\frac{1}{\sqrt{1 - x^2}\left( 2 + 3 \sin^{- 1} x \right)} dx\]
\[\int\frac{\log\left( 1 + \frac{1}{x} \right)}{x \left( 1 + x \right)} dx\]
\[\int\left( \frac{x + 1}{x} \right) \left( x + \log x \right)^2 dx\]
\[\int 5^{5^{5^x}} 5^{5^x} 5^x dx\]
\[\int\frac{2x - 1}{\left( x - 1 \right)^2} dx\]
\[\int\frac{1}{x^2 - 10x + 34} dx\]
\[\int\frac{1}{\sqrt{\left( 1 - x^2 \right)\left\{ 9 + \left( \sin^{- 1} x \right)^2 \right\}}} dx\]
\[\int\frac{x - 1}{3 x^2 - 4x + 3} dx\]
\[\int\frac{\left( x - 1 \right)^2}{x^2 + 2x + 2} dx\]
\[\int\frac{x + 2}{\sqrt{x^2 + 2x - 1}} \text{ dx }\]
\[\int\frac{5x + 3}{\sqrt{x^2 + 4x + 10}} \text{ dx }\]
\[\int\frac{1}{\cos 2x + 3 \sin^2 x} dx\]
\[\int x^3 \cos x^2 dx\]
\[\int \sin^{- 1} \sqrt{x} \text{ dx }\]
\[\int\left( x + 1 \right) \text{ e}^x \text{ log } \left( x e^x \right) dx\]
\[\int \cos^3 \sqrt{x}\ dx\]
\[\int\frac{x^2 + x - 1}{x^2 + x - 6} dx\]
\[\int\frac{x^2 + 1}{x\left( x^2 - 1 \right)} dx\]
\[\int\sqrt{\cot \text{θ} d } \text{ θ}\]
\[\int\frac{1}{\left( x - 1 \right) \sqrt{x + 2}} \text{ dx }\]
\[\int\frac{x}{\left( x - 3 \right) \sqrt{x + 1}} dx\]
\[\int\left( x - 1 \right) e^{- x} dx\] is equal to
\[\int \cot^4 x\ dx\]
\[\int \sec^6 x\ dx\]
\[\int \tan^5 x\ \sec^3 x\ dx\]
\[\int \sin^{- 1} \left( 3x - 4 x^3 \right) \text{ dx}\]
Find : \[\int\frac{e^x}{\left( 2 + e^x \right)\left( 4 + e^{2x} \right)}dx.\]
