Advertisements
Advertisements
Question
\[\int\frac{\left\{ e^{\sin^{- 1} }x \right\}^2}{\sqrt{1 - x^2}} dx\]
Solution
\[\int\frac{\left( e^\{sin^{- 1} x \right)^2}{\sqrt{1 - x^2}} dx\]
` Let e^{sin-1 _x }= t `
Differentiating both sides w . r . t . x,
`e^{sin-1 _x } × 1 / \sqrt{ 1 - x^2 } ` dx = dt
` Now , ∫ (e^{sin-1 _ x }) ^2/ \sqrt{1-x^2} ` dx
` ∫ e^{sin-1 _x } . {e^{sin-1 _ x }}/ \sqrt{1-x^2} ` dx
` ∫ t . dt
\[ = \frac{t^2}{2} + C\]
` (e^{sin-1 _x })^2 /2 + C`
APPEARS IN
RELATED QUESTIONS
Evaluate : `int_0^3dx/(9+x^2)`
Integrate the following w.r.t. x `(x^3-3x+1)/sqrt(1-x^2)`
Evaluate the following integrals:
\[\int\frac{\cot x}{\sqrt{\sin x}} dx\]
Evaluate the following integrals:
Evaluate the following integrals:
Evaluate the following integrals:
Evaluate the following integral :-
Evaluate the following integral:
Evaluate the following integrals:
Evaluate the following integral:
Write a value of
Evaluate:
Evaluate:\[\int\frac{\sin \sqrt{x}}{\sqrt{x}} \text{ dx }\]
Evaluate:\[\int \sec^2 \left( 7 - 4x \right) \text{ dx }\]
Evaluate: \[\int\frac{1}{\sqrt{1 - x^2}} \text{ dx }\]
Write the value of\[\int\sec x \left( \sec x + \tan x \right)\text{ dx }\]
Evaluate: \[\int\frac{1}{x^2 + 16}\text{ dx }\]
Evaluate: \[\int\frac{x + \cos6x}{3 x^2 + \sin6x}\text{ dx }\]
Evaluate:
Evaluate the following:
`int sqrt(1 + x^2)/x^4 "d"x`
Evaluate the following:
`int (3x - 1)/sqrt(x^2 + 9) "d"x`
Evaluate the following:
`int_1^2 ("d"x)/sqrt((x - 1)(2 - x))`
