{1}{{8+3x-x²} - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.4
Integrate the functions in Exercises 86 to 108.

Question : 99 of 271

Marks: +1, -0

\frac{1}{\sqrt{8+3x-x^2}}

Solution:

Let

I=\int\frac{dx}{\sqrt{8+3x-x^2}}

=\int\frac{dx}{\sqrt{8-(x^2-3x)}}

=\int\frac{dx}{\sqrt{8-\left(x^2-2\cdot\frac{3}{2}\cdot x+\frac{9}{4}\right)+\frac{9}{4}}}

=\int\frac{dx}{\sqrt{\frac{41}{4}-\left(x-\frac{3}{2}\right)^2}}

=\int\frac{dx}{\sqrt{\left(\frac{\sqrt{41}}{4}\right)^2-\left(x-\frac{3}{2}\right)^2}}

=\sin^{-1}\left(\frac{x-\frac{3}{2}}{\frac{\sqrt{41}}{2}}\right)+C

=\sin^{-1}\left(\frac{2x-3}{\sqrt{41}}\right)+C

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