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  • Integrate the functions in Exercises 1 to 9. root of x^2 + 4x - 5

Integrate the functions in Exercises 1 to 9.

    Q6.    \sqrt{x^2 + 4x - 5}

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best_answer

Given function \sqrt{x^2 + 4x - 5},

So, let us consider the function to be;

I = \int\sqrt{x^2+4x-5}dx

 a= \int\sqrt{(x^2+4x+4)-9}dx = \int\sqrt{(x+2)^2 -(3)^2}dx

And we know that, \int \sqrt{x^2-a^2}dx = \frac{x}{2}\sqrt{x^2-a^2}-\frac{a^2}{2}\log|x+\sqrt{x^2-a^2}|+C

\therefore I = \frac{x+2}{2}\sqrt{x^2+4x-5}-\frac{9}{2}\log\left | (x+2)+ \sqrt{x^2+4x-5} \right |+C

 

Posted by

Divya Prakash Singh

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