Advertisements
Advertisements
प्रश्न
\[\int x^2 \text{ cos x dx }\]
योग
Advertisements
उत्तर
\[\int x^2 \text{ cos x dx }\]
` " Taking x"^2" as the first function and cos x as the second function . " `
\[ = x^2 \int\text{ cos x dx } - \int\left\{ \frac{d}{dx}\left( x^2 \right)\int\text{ cos x dx }\right\}dx\]
\[ = x^2 \sin x - \int2x \text{ sin x dx }\]
\[ = x^2 \sin x - 2\left[ x\int\sin x - \int\left\{ \frac{d}{dx}\left( x \right)\int\text{ sin x dx }\right\}dx \right]\]
\[ = x^2 \sin x + 2x\cos x - 2\int\text{ cos x dx }\]
\[ = x^2 \sin x + 2x \cos x - 2 \sin x + C\]
shaalaa.com
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
\[\int\left( 2 - 3x \right) \left( 3 + 2x \right) \left( 1 - 2x \right) dx\]
\[\int\sqrt{x}\left( x^3 - \frac{2}{x} \right) dx\]
\[\int\frac{\cos^2 x - \sin^2 x}{\sqrt{1} + \cos 4x} dx\]
\[\int\frac{\cos x}{1 + \cos x} dx\]
\[\int\frac{1}{\sqrt{x + a} + \sqrt{x + b}} dx\]
\[\int\frac{x^3}{x - 2} dx\]
\[\int\frac{x^2 + x + 5}{3x + 2} dx\]
\[\int\sqrt{\frac{1 + \cos 2x}{1 - \cos 2x}} dx\]
` ∫ {sec x "cosec " x}/{log ( tan x) }` dx
\[\int\frac{\cos 4x - \cos 2x}{\sin 4x - \sin 2x} dx\]
\[\int\frac{1 + \cot x}{x + \log \sin x} dx\]
\[\int\frac{\tan x}{\sqrt{\cos x}} dx\]
\[\int\frac{x}{3 x^4 - 18 x^2 + 11} dx\]
\[\int\frac{e^x}{\left( 1 + e^x \right)\left( 2 + e^x \right)} dx\]
\[\int\frac{1}{\sqrt{7 - 6x - x^2}} dx\]
\[\int\frac{2x + 1}{\sqrt{x^2 + 4x + 3}} \text{ dx }\]
\[\int\frac{1}{\sin x + \sqrt{3} \cos x} \text{ dx }\]
\[\int\frac{1}{5 + 7 \cos x + \sin x} dx\]
\[\int\left( x + 1 \right) \text{ e}^x \text{ log } \left( x e^x \right) dx\]
\[\int \tan^{- 1} \left( \sqrt{x} \right) \text{dx }\]
\[\int e^x \left( \frac{x - 1}{2 x^2} \right) dx\]
\[\int e^x \sec x \left( 1 + \tan x \right) dx\]
\[\int x^2 \sqrt{a^6 - x^6} \text{ dx}\]
\[\int\frac{1}{x\left( x^n + 1 \right)} dx\]
\[\int\frac{1}{x \left( x^4 + 1 \right)} dx\]
\[\int\frac{3}{\left( 1 - x \right) \left( 1 + x^2 \right)} dx\]
\[\int\frac{1}{\left( x^2 + 1 \right) \sqrt{x}} \text{ dx }\]
\[\int\frac{x^3}{x + 1}dx\] is equal to
\[\int\frac{x + 2}{\left( x + 1 \right)^3} \text{ dx }\]
\[\int \cot^4 x\ dx\]
\[\int \sin^5 x\ dx\]
\[\int\sqrt{a^2 - x^2}\text{ dx }\]
\[\int\sqrt{3 x^2 + 4x + 1}\text{ dx }\]
\[\int\frac{x^2 + x + 1}{\left( x + 1 \right)^2 \left( x + 2 \right)} \text{ dx}\]
Find : \[\int\frac{dx}{\sqrt{3 - 2x - x^2}}\] .
\[\int\frac{x + 3}{\left( x + 4 \right)^2} e^x dx =\]
Find: `int (3x +5)/(x^2+3x-18)dx.`
