Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefiite Integrals Excercise Fill in the Blanks Question 6

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefiite Integrals Excercise Fill in the Blanks Question 6

Answers (1)

Answer:

\frac{e^{x}}{x+4}+c

Hint:

Simplify the function and then integrate it.

Solution:

\begin{aligned} &I=\int \frac{x+3}{(x+4)^{2}} e^{x} d x \\ &I=\int \frac{x+4-1}{(x+4)^{2}} e^{x} d x \\ &I=I=\int\left[\frac{1}{x+4}-\frac{1}{(x+4)^{2}}\right] e^{x} d x \end{aligned}

 

Let  f(x)=\frac{1}{x+4}

 

then  {f}'\left (x \right )=-\frac{1}{\left ( x+4 \right )^{2}}

\begin{aligned} &\Rightarrow I=\int\left[f(x)+f^{\prime}(x)\right] e^{x} d x \\ &\Rightarrow I= \int\left[f(x)+f^{\prime}(x)\right] e^{x} d x \\ &\Rightarrow I=f(x) e^{x}+c \\ &I=\frac{e^{x}}{x+4}+c \end{aligned}

Posted by

infoexpert27

View full answer

Crack CUET with india's "Best Teachers"

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

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years

Latest Question