Advertisements
Advertisements
प्रश्न
\[\int \sec^2 x \cos^2 2x \text{ dx }\]
योग
Advertisements
उत्तर
\[\int\left( \sec^2 x \cdot \cos^2 2x \right)dx\]
\[ = \int \sec^2 x \times \left( 2 \cos^2 x - 1 \right)^2 dx\]
\[ = \int \sec^2 x \left[ 4 \cos^4 x - 4 \cos^2 x + 1 \right]dx\]
\[ \Rightarrow \int\left( 4 \cos^2 x - 4 + \sec^2 x \right)dx\]
\[ = 4\int \cos^2 x \text{ dx } + \int \sec^2 x \text{ dx }- 4\int dx\]
\[ \Rightarrow 4\int\left( \frac{1 + \cos 2x}{2} \right)dx + \int \sec^2 x - 4\int dx\]
\[ \Rightarrow 2 \left[ x + \frac{\sin 2x}{2} \right] + \tan x - 4x + C\]
\[ \Rightarrow \sin 2x + \tan x - 2x + C\]
shaalaa.com
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
\[\int\frac{\left( 1 + x \right)^3}{\sqrt{x}} dx\]
\[\int\frac{1}{1 - \sin x} dx\]
\[\int \sin^{- 1} \left( \frac{2 \tan x}{1 + \tan^2 x} \right) dx\]
If f' (x) = x − \[\frac{1}{x^2}\] and f (1) \[\frac{1}{2}, find f(x)\]
\[\int\frac{x \sin^{- 1} x^2}{\sqrt{1 - x^4}} dx\]
\[\int\frac{x^5}{\sqrt{1 + x^3}} dx\]
\[\int\frac{x^2 + 3x + 1}{\left( x + 1 \right)^2} dx\]
\[\int \sec^4 2x \text{ dx }\]
\[\int \cot^n {cosec}^2 \text{ x dx } , n \neq - 1\]
\[\int\frac{1}{\sin x \cos^3 x} dx\]
\[\int\frac{x^4 + 1}{x^2 + 1} dx\]
\[\int\frac{e^x}{\sqrt{16 - e^{2x}}} dx\]
\[\int\frac{x^2 + x + 1}{x^2 - x + 1} \text{ dx }\]
\[\int\frac{2x + 1}{\sqrt{x^2 + 4x + 3}} \text{ dx }\]
\[\int\frac{5x + 3}{\sqrt{x^2 + 4x + 10}} \text{ dx }\]
\[\int\frac{1}{\left( \sin x - 2 \cos x \right)\left( 2 \sin x + \cos x \right)} \text{ dx }\]
\[\int\frac{1}{2 + \sin x + \cos x} \text{ dx }\]
\[\int\frac{1}{1 - \tan x} \text{ dx }\]
\[\int x^2 \text{ cos x dx }\]
\[\int \log_{10} x\ dx\]
\[\int x^3 \tan^{- 1}\text{ x dx }\]
\[\int\frac{\sqrt{1 - \sin x}}{1 + \cos x} e^{- x/2} \text{ dx }\]
\[\int\sqrt{3 - x^2} \text{ dx}\]
\[\int\frac{x + 1}{x \left( 1 + x e^x \right)} dx\]
\[\int\sqrt{\cot \text{θ} d } \text{ θ}\]
\[\int\frac{x^2 - 1}{x^4 + 1} \text{ dx }\]
\[\int\frac{1}{\left( x - 1 \right) \sqrt{x + 2}} \text{ dx }\]
\[\int\frac{1}{\left( x - 1 \right) \sqrt{2x + 3}} \text{ dx }\]
Write a value of
\[\int e^{3 \text{ log x}} x^4\text{ dx}\]
` \int \text{ x} \text{ sec x}^2 \text{ dx is equal to }`
\[\int\frac{\sin x - \cos x}{\sqrt{\sin 2x}} \text{ dx }\]
\[\int\frac{1}{\sqrt{x^2 + a^2}} \text{ dx }\]
\[\int\frac{1}{a + b \tan x} \text{ dx }\]
\[\int\frac{\log x}{x^3} \text{ dx }\]
\[\int\frac{1}{x \sqrt{1 + x^n}} \text{ dx}\]
Find : \[\int\frac{dx}{\sqrt{3 - 2x - x^2}}\] .
Find : \[\int\frac{e^x}{\left( 2 + e^x \right)\left( 4 + e^{2x} \right)}dx.\]
