{1}{{7-6x-x²} - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

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

Question : 97 of 271

Marks: +1, -0

\frac{1}{\sqrt{7-6x-x^2}}

Solution:

Let

I=\int \frac{1}{\sqrt{7-6x-x^2}} dx

=\int \frac{1}{\sqrt{7-(x^2-6x)}} dx

=\int \frac{dx}{\sqrt{16-(x^2+6x+9)}}

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

=\sin^{-1}\left(\frac{x+3}{4}\right)+C

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