Advertisements
Advertisements
प्रश्न
\[\int x^3 \sin x^4 dx\]
बेरीज
Advertisements
उत्तर
\[\int x^3 \cdot \sin x^4 dx\]
\[\text{Let x}^4 = t\]
\[ \Rightarrow 4 x^3 = \frac{dt}{dx}\]
\[ \Rightarrow x^3 dx = \frac{dt}{4}\]
\[Now, \int x^3 \cdot \text{sin x^4} \text{dx}\]
\[ = \frac{1}{4}\int\text{sin t dt}\]
\[ = \frac{1}{4}\left[ - \cos t \right] + C\]
\[ = \frac{1}{4}\left[ - \cos x^4 \right] + C\]
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
APPEARS IN
संबंधित प्रश्न
\[\int\frac{\cos x}{1 + \cos x} dx\]
If f' (x) = x − \[\frac{1}{x^2}\] and f (1) \[\frac{1}{2}, find f(x)\]
If f' (x) = 8x3 − 2x, f(2) = 8, find f(x)
\[\int\frac{x + 1}{\sqrt{2x + 3}} dx\]
\[\int\frac{2x + 1}{\sqrt{3x + 2}} dx\]
\[\int\frac{\sec x \tan x}{3 \sec x + 5} dx\]
\[\int\frac{\sin 2x}{\left( a + b \cos 2x \right)^2} dx\]
\[\int\frac{x \sin^{- 1} x^2}{\sqrt{1 - x^4}} dx\]
\[\int\frac{\cos^5 x}{\sin x} dx\]
\[\int x^2 \sqrt{x + 2} \text{ dx }\]
\[\int \sin^5 x \cos x \text{ dx }\]
\[\int\frac{1}{\sin^3 x \cos^5 x} dx\]
Evaluate the following integrals:
\[\int\frac{x^7}{\left( a^2 - x^2 \right)^5}dx\]
\[\int\frac{\sec^2 x}{1 - \tan^2 x} dx\]
\[\int\frac{3 x^5}{1 + x^{12}} dx\]
\[\int\frac{x}{\sqrt{x^4 + a^4}} dx\]
\[\int\frac{\cos x}{\sqrt{4 + \sin^2 x}} dx\]
\[\int\frac{\cos 2x}{\sqrt{\sin^2 2x + 8}} dx\]
\[\int\frac{\sin 2x}{\sqrt{\sin^4 x + 4 \sin^2 x - 2}} dx\]
` ∫ \sqrt{"cosec x"- 1} dx `
\[\int\frac{x + 1}{\sqrt{x^2 + 1}} dx\]
\[\int\frac{1}{\sin^2 x + \sin 2x} \text{ dx }\]
\[\int x e^{2x} \text{ dx }\]
\[\int \sin^{- 1} \left( 3x - 4 x^3 \right) \text{ dx }\]
\[\int\left( e^\text{log x} + \sin x \right) \text{ cos x dx }\]
\[\int \sin^{- 1} \sqrt{\frac{x}{a + x}} \text{ dx }\]
\[\int e^x \left( \frac{1}{x^2} - \frac{2}{x^3} \right) dx\]
\[\int\left\{ \tan \left( \log x \right) + \sec^2 \left( \log x \right) \right\} dx\]
\[\int(2x + 5)\sqrt{10 - 4x - 3 x^2}dx\]
\[\int\frac{1}{\cos x + \sqrt{3} \sin x} \text{ dx } \] is equal to
\[\int\frac{1 - x^4}{1 - x} \text{ dx }\]
\[\int\frac{1}{e^x + e^{- x}} dx\]
\[\int\frac{1}{\text{ cos }\left( x - a \right) \text{ cos }\left( x - b \right)} \text{ dx }\]
\[\int\sqrt{\sin x} \cos^3 x\ \text{ dx }\]
\[\int\frac{\sin^5 x}{\cos^4 x} \text{ dx }\]
\[\int \sin^{- 1} \sqrt{x}\ dx\]
\[\int \cos^{- 1} \left( 1 - 2 x^2 \right) \text{ dx }\]
\[\int\frac{x \sin^{- 1} x}{\left( 1 - x^2 \right)^{3/2}} \text{ dx}\]
\[\int\frac{\sqrt{1 - \sin x}}{1 + \cos x} e^{- x/2} \text{ dx}\]
