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NCERT Class XII Mathematics Chapter - - Solutions

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Exercise - 7.7
Integrate the functions in Exercises 158 to 166.
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Question : 163 of 271
Marks: +1, -0
x2+4x−5\sqrt{x^2+4x-5}
Solution:  
Let I=x2+4x−5dxI=\sqrt{x^2+4x-5}dx
=(x2+4x+4)−9dx=\sqrt{(x^2+4x+4)-9}dx
=∫(x+2)2−(3)2dx=\int\sqrt{(x+2)^2-(3)^2}dx
=x+22(x+2)2−(3)2−92log⁡∣(x+2)+(x+2)2−(3)2∣+C=\frac{x+2}{2}\sqrt{(x+2)^2-(3)^2}-\frac{9}{2}\log\left|(x+2)+\sqrt{(x+2)^2-(3)^2}\right|+C
=x+22x2+4x−5−92log⁡∣(x+2)+x2+4x−5∣+C=\frac{x+2}{2}\sqrt{x^2+4x-5}-\frac{9}{2}\log\left|(x+2)+\sqrt{x^2+4x-5}\right|+C
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