Advertisements
Advertisements
प्रश्न
\[\int\frac{\tan x}{\sqrt{\cos x}} dx\]
बेरीज
Advertisements
उत्तर
\[\int\frac{\tan x}{\sqrt{\cos x}}dx\]
\[ \Rightarrow \int\frac{\sin x}{\cos x \sqrt{\cos x}} dx\]
\[ \Rightarrow \int\frac{\sin x}{\cos {}^\frac{3}{2} x}dx\]
\[Let \cos x = t\]
\[ \Rightarrow - \text{sin x dx }= dt\]
\[ \Rightarrow \sin x = - \frac{dt}{dx}\]
\[Now, \int\frac{\sin x}{\cos {}^\frac{3}{2} x}dx\]
\[ = \int - \frac{1}{t^\frac{3}{2}}dt\]
\[ = - \int t^{- \frac{3}{2}} dt\]
\[ = - \left[ \frac{t^{- \frac{3}{2} + 1}}{\frac{- 3}{2} + 1} \right] + C\]
\[ = \frac{2}{\sqrt{t}} + C\]
\[ = \frac{2}{\sqrt{\cos x}} + C\]
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
APPEARS IN
संबंधित प्रश्न
\[\int\left( x^e + e^x + e^e \right) dx\]
\[\int\sqrt{x}\left( 3 - 5x \right) dx\]
\[\int\left( \sec^2 x + {cosec}^2 x \right) dx\]
If f' (x) = x + b, f(1) = 5, f(2) = 13, find f(x)
\[\int\frac{1}{2 - 3x} + \frac{1}{\sqrt{3x - 2}} dx\]
\[\int\frac{1}{\sqrt{2x + 3} + \sqrt{2x - 3}} dx\]
Integrate the following integrals:
\[\int\text{sin 2x sin 4x sin 6x dx} \]
\[\int\sqrt{\frac{1 - \sin 2x}{1 + \sin 2x}} dx\]
\[\int\frac{\cos x}{2 + 3 \sin x} dx\]
\[\int\sqrt{1 + e^x} . e^x dx\]
\[\int \tan^{3/2} x \sec^2 \text{x dx}\]
\[\int\frac{x^5}{\sqrt{1 + x^3}} dx\]
\[\int\frac{1}{\sqrt{x} + x} \text{ dx }\]
\[\int\left( 2 x^2 + 3 \right) \sqrt{x + 2} \text{ dx }\]
\[\int \sin^5 x \text{ dx }\]
\[\int \sin^3 x \cos^5 x \text{ dx }\]
\[\int\frac{1}{a^2 - b^2 x^2} dx\]
\[\int\frac{x^2 - 1}{x^2 + 4} dx\]
\[\int\frac{x}{\sqrt{x^4 + a^4}} dx\]
\[\int\frac{x + 7}{3 x^2 + 25x + 28}\text{ dx}\]
\[\int\frac{2x + 1}{\sqrt{x^2 + 2x - 1}}\text{ dx }\]
\[\int\frac{1}{3 + 2 \cos^2 x} \text{ dx }\]
\[\int\frac{1}{1 - 2 \sin x} \text{ dx }\]
\[\int\frac{1}{3 + 2 \sin x + \cos x} \text{ dx }\]
\[\int x^2 \sin^2 x\ dx\]
` ∫ x tan ^2 x dx
\[\int x^2 \sqrt{a^6 - x^6} \text{ dx}\]
\[\int\sqrt{2x - x^2} \text{ dx}\]
\[\int\frac{x^2 + x - 1}{x^2 + x - 6} dx\]
\[\int\frac{1}{x\left[ 6 \left( \log x \right)^2 + 7 \log x + 2 \right]} dx\]
\[\int\frac{x}{\left( x^2 - a^2 \right) \left( x^2 - b^2 \right)} dx\]
\[\int\frac{1}{\sin x \left( 3 + 2 \cos x \right)} dx\]
\[\int\left( x - 1 \right) e^{- x} dx\] is equal to
The value of \[\int\frac{\sin x + \cos x}{\sqrt{1 - \sin 2x}} dx\] is equal to
\[\int \cos^5 x\ dx\]
\[\int\frac{\sqrt{a} - \sqrt{x}}{1 - \sqrt{ax}}\text{ dx }\]
\[\int\frac{1}{\sin x \left( 2 + 3 \cos x \right)} \text{ dx }\]
\[\int\sqrt{3 x^2 + 4x + 1}\text{ dx }\]
\[\int\frac{x^2}{\sqrt{1 - x}} \text{ dx }\]
\[\int \cos^{- 1} \left( 1 - 2 x^2 \right) \text{ dx }\]
