Advertisement Remove all ads

∫ 1 √ 7 − 6 X − X 2 D X - Mathematics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Sum
\[\int\frac{1}{\sqrt{7 - 6x - x^2}} dx\]
Advertisement Remove all ads

Solution

\[\int\frac{dx}{\sqrt{7 - 6x - x^2}}\]
\[ = \int\frac{dx}{\sqrt{7 - \left( x^2 + 6x \right)}}\]
\[ = \int\frac{dx}{\sqrt{7 - \left[ x^2 + 6x + 3^2 - 3^2 \right]}}\]
\[ = \int\frac{dx}{\sqrt{7 + 9 - \left( x + 3 \right)^2}}\]
\[ = \int\frac{dx}{\sqrt{4^2 - \left( x + 3 \right)^2}}\]
\[ = \sin^{- 1} \left( \frac{x + 3}{4} \right) + C\]

Concept: Indefinite Integral Problems
  Is there an error in this question or solution?

APPEARS IN

RD Sharma Class 12 Maths
Chapter 19 Indefinite Integrals
Exercise 19.17 | Q 8 | Page 93

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×