Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
Advertisement Remove all ads

2 ∫ 1 X + 3 X ( X + 2 ) D X - Mathematics

Sum

\[\int\limits_1^2 \frac{x + 3}{x\left( x + 2 \right)} dx\]

Advertisement Remove all ads

Solution

\[\int_1^2 \frac{x + 3}{x\left( x + 2 \right)} d x\]

\[ = \int_1^2 \frac{x + 2 + 1}{x\left( x + 2 \right)} d x\]

\[ = \int_1^2 \frac{1}{x}dx + \int_1^2 \frac{1}{x\left( x + 2 \right)}dx\]

\[ = \int_1^2 \frac{1}{x}dx + \frac{1}{2} \int_1^2 \frac{\left( x + 2 \right) - x}{x\left( x + 2 \right)}dx\]

\[ = \int_1^2 \frac{1}{x}dx + \frac{1}{2} \int_1^2 \frac{1}{x}dx - \frac{1}{2} \int_1^2 \frac{1}{x + 2}dx\]

\[ = \frac{3}{2} \int_1^2 \frac{1}{x}dx - \frac{1}{2} \int_1^2 \frac{1}{x + 2}dx\]

\[ = \frac{3}{2} \left[ \log x \right]_1^2 - \frac{1}{2} \left[ \log\left( x + 2 \right) \right]_1^2 \]

\[ = \frac{3}{2}\log2 - \frac{1}{2}\log4 + \frac{1}{2}\log3\]

\[ = \frac{3}{2}\log2 - \log2 + \frac{1}{2}\log3\]

\[ = \frac{1}{2}\log2 + \frac{1}{2}\log3\]

\[ = \frac{1}{2}\log6\]

Concept: Definite Integrals Problems
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 12 Maths
Chapter 20 Definite Integrals
Revision Exercise | Q 26 | Page 121
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×