Solving Indefinite Integrals: "int (1/(sqrt -x^2 -2x))dx

Thread starter Atilla1982
Start date Nov 15, 2005
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Indefinite Indefinite integral Integral

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SUMMARY

The forum discussion focuses on solving the indefinite integral of the function int (1/(sqrt(-x^2 - 2x)))dx. The user successfully rewrites the expression as int (1/(sqrt(1 - (x + 1)^2))) dt after substituting t = x + 1. The discussion emphasizes the importance of recognizing the derivative of the arcsine function to proceed with the integration. The key conclusion is that understanding trigonometric substitutions is essential for solving integrals involving square roots of quadratic expressions.

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Understanding of indefinite integrals
Familiarity with trigonometric substitutions
Knowledge of the arcsine function and its derivative
Basic algebraic manipulation skills

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Study the properties of the arcsine function and its applications in integration
Learn about trigonometric substitutions in integral calculus
Practice solving integrals involving square roots of quadratic expressions
Explore advanced techniques in integration, such as integration by parts and partial fractions

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Students of calculus, mathematics educators, and anyone seeking to improve their skills in solving indefinite integrals, particularly those involving trigonometric functions and substitutions.

Nov 15, 2005

Atilla1982

I have:

int (1/(sqrt -x^2 -2x))dx

so I rewrite (-x^2-2x) --> 1-(x+1)^2 and swap those two.

then I say t=x+1, and substitute that in.

So now I have:

int (1/(sqrt 1-t^2)) dt

Here I get stuck, can anyone please help?