{x²+3x} - NCERT Class XII Mathematics Chapter - - Solutions

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.7
Integrate the functions in Exercises 158 to 166.

Question : 165 of 271

Marks: +1, -0

\sqrt{x^2+3x}

Solution:

Let

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

= \int \sqrt{ \left(x + \frac{3}{2}\right)^2 - \left(\frac{3}{2}\right)^2 } dx

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

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

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