Advertisements
Advertisements
Question
\[\int\frac{x}{\sqrt{4 - x^4}} dx\]
Sum
Solution
` ∫ { x dx }/{\sqrt{4 - x^4}} `
` ∫ { x dx }/{\sqrt{2^2 - (x^2)^2}} `
\[\text{ let } x^2 = t\]
\[ \Rightarrow \text{ 2x dx } = dt\]
\[ \Rightarrow \text{ x dx } = \frac{dt}{2}\]
Now, ` ∫ { x dx }/{\sqrt{2^2 - (x^2)^2}} `
\[ = \frac{1}{2}\int\frac{dt}{\sqrt{2^2 - t^2}}\]
\[ = \frac{1}{2} \times \sin^{- 1} \left( \frac{1}{2} \right) + C\]
\[ = \frac{1}{2} \sin^{- 1} \left( \frac{x^2}{2} \right) + C\]
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
\[\int\frac{1}{1 - \sin x} dx\]
\[\int\frac{1 - \cos x}{1 + \cos x} dx\]
If f' (x) = a sin x + b cos x and f' (0) = 4, f(0) = 3, f
\[\left( \frac{\pi}{2} \right)\] = 5, find f(x)
\[\int\frac{1}{2 - 3x} + \frac{1}{\sqrt{3x - 2}} dx\]
\[\int\frac{1}{\text{cos}^2\text{ x }\left( 1 - \text{tan x} \right)^2} dx\]
\[\int\frac{\cos^3 x}{\sqrt{\sin x}} dx\]
\[\int\sqrt {e^x- 1} \text{dx}\]
\[\int\frac{\sin^5 x}{\cos^4 x} \text{ dx }\]
\[\int\frac{1}{\sqrt{a^2 + b^2 x^2}} dx\]
\[\int\frac{1}{\sqrt{a^2 - b^2 x^2}} dx\]
\[\int\frac{\cos x}{\sin^2 x + 4 \sin x + 5} dx\]
\[\int\frac{1}{\sqrt{8 + 3x - x^2}} dx\]
\[\int\frac{1}{\sqrt{5 x^2 - 2x}} dx\]
\[\int\frac{\cos x}{\sqrt{4 + \sin^2 x}} dx\]
\[\int\frac{\sin x}{\sqrt{4 \cos^2 x - 1}} dx\]
\[\int\frac{2x}{2 + x - x^2} \text{ dx }\]
\[\int\frac{x^2}{x^2 + 7x + 10} dx\]
\[\int\frac{1}{1 - \tan x} \text{ dx }\]
\[\int\frac{4 \sin x + 5 \cos x}{5 \sin x + 4 \cos x} \text{ dx }\]
\[\int x^2 \tan^{- 1} x\text{ dx }\]
\[\int \tan^{- 1} \left( \sqrt{x} \right) \text{dx }\]
\[\int\frac{x \sin^{- 1} x}{\sqrt{1 - x^2}} dx\]
\[\int\left( x + 2 \right) \sqrt{x^2 + x + 1} \text{ dx }\]
\[\int\frac{5 x^2 + 20x + 6}{x^3 + 2 x^2 + x} dx\]
Evaluate the following integral:
\[\int\frac{x^2}{\left( x^2 + a^2 \right)\left( x^2 + b^2 \right)}dx\]
Evaluate the following integral:
\[\int\frac{x^2}{1 - x^4}dx\]
\[\int x^{\sin x} \left( \frac{\sin x}{x} + \cos x . \log x \right) dx\] is equal to
If \[\int\frac{\cos 8x + 1}{\tan 2x - \cot 2x} dx\]
\[\int\frac{\cos 2x - 1}{\cos 2x + 1} dx =\]
\[\int\frac{1}{e^x + e^{- x}} dx\]
\[\int\frac{1}{\text{ sin} \left( x - a \right) \text{ sin } \left( x - b \right)} \text{ dx }\]
\[\int\frac{\sin x}{\cos 2x} \text{ dx }\]
\[\int \cot^4 x\ dx\]
\[\int\frac{x^3}{\left( 1 + x^2 \right)^2} \text{ dx }\]
\[\int x \sin^5 x^2 \cos x^2 dx\]
\[\int\frac{\sin x}{\sqrt{\cos^2 x - 2 \cos x - 3}} \text{ dx }\]
\[\int\frac{1}{a + b \tan x} \text{ dx }\]
\[\int\frac{1 + x^2}{\sqrt{1 - x^2}} \text{ dx }\]
\[\int \tan^{- 1} \sqrt{x}\ dx\]
\[\int\frac{x + 3}{\left( x + 4 \right)^2} e^x dx =\]
