Get Answers to all your Questions

header-bg qa

Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise 18.19 Question 13 Maths Textbook Solution.

Answers (1)

Answer:

\frac{1}{3} \log |3 x-2|+c

Hint: Solve integration by equation

Given:

\begin{aligned} &\int \frac{x+5}{3 x^{2}+13 x-10} d x \\ &=\int \frac{x+5}{3 x^{2}+15 x-2 x-10} d x \\ &=\int \frac{x+5}{3 x(x+5)-2(x+5)} d x \end{aligned}

\begin{aligned} &=\int \frac{x+5}{(3 x-2)(x+5)} d x \\ &=\int \frac{d x}{3 x-2} \end{aligned}                                            .........(1)

                       \begin{aligned} &\text { Let, } 3 x-2=t \\ &\qquad \begin{array}{r} 3 d x=d t \\ d x=\frac{d t}{3} \end{array} \end{aligned}

\begin{aligned} &=\int \frac{d t}{3 t}+c \\ &=\frac{1}{3} \log |3 x-2|+c \end{aligned}

Posted by

infoexpert21

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads