Advertisements
Advertisements
प्रश्न
Advertisements
उत्तर
\[\int x^2 \text{ cos x dx }\]
` "Taking x"^2" as the first function and cos x as the second function " . `
\[ = x^2 \int\cos x dx - \int\left( \frac{d}{dx} x^2 \int\text{ cos x dx } \right)dx\]
\[ = x^2 \sin x - \int2x \text{ sin x dx }\]
\[ = x^2 \sin x - 2\left[ x\int\sin x - \int\left\{ \frac{d}{dx}\left( x \right)\int\text{ sin x dx } \right\}dx \right]\]
\[ = x^2 \sin x - 2\left[ - x\cos x + \int\text{ cos x dx } \right]\]
\[ = x^2 \sin x + 2x \cos x - 2 \sin x + C\]
APPEARS IN
संबंधित प्रश्न
If f' (x) = x − \[\frac{1}{x^2}\] and f (1) \[\frac{1}{2}, find f(x)\]
If `int(2x^(1/2))/(x^2) dx = k . 2^(1/x) + C`, then k is equal to ______.
\[\int\frac{1 + \sin x}{\sin x \left( 1 + \cos x \right)} \text{ dx }\]
Find : \[\int\frac{e^x}{\left( 2 + e^x \right)\left( 4 + e^{2x} \right)}dx.\]
\[\int\frac{x + 3}{\left( x + 4 \right)^2} e^x dx =\]
