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  • Integrate the functions in Exercises 1 to 9. root of x^2 + 3x

Integrate the functions in Exercises 1 to 9.

    Q8.    \sqrt{x^2 + 3x}

Answers (1)

best_answer

Given function \sqrt{x^2 + 3x},

So, let us consider the function to be;

I = \int\sqrt{x^2+3x}dx

= \int\sqrt{x^2+3x+\frac{9}{4}-\frac{9}{4}}dx

= \int\sqrt{\left ( x+\frac{3}{2} \right )^2-\left ( \frac{3}{2} \right )^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+\frac{3}{2}}{2}\sqrt{x^2+3x}-\frac{\frac{9}{4}}{2}\log \left | \left ( x+\frac{3}{2} \right )+\sqrt{x^2+3x} \right |+C

= \frac{2x+3}{4}\sqrt{x^2+3x}-\frac{9}{8}\log\left | \left ( x+\frac{3}{2} \right )+\sqrt{x^2+3x} \right |+C

Posted by

Divya Prakash Singh

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