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 R.D. Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise 18.3 Question 14 Maths Textbook Solution.

Need Solution for R.D. Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise 18.3 Question 14 Maths Textbook Solution.

Answers (1)

best_answer

Answer: \frac{e^{3 x}}{3}+e^{2 x}+e^{x}+c

Hint: \text { To solve this } \int x^{n} d x \text { formula }

Given: \int\left(e^{x}+1\right)^{2} e^{x} d x

Solution: \int\left(e^{x}+1\right)^{2} e^{x} d x

\begin{aligned} &=\int\left(e^{2 x}+1+2 e^{x}\right) e^{x} d x \quad\left[(a+b)^{2}=a^{2}+b^{2}+2 a b\right] \\ &=\int\left(e^{3 x}+2 e^{2 x}+e^{x}\right) d x \end{aligned}

\begin{aligned} &=\int\left(e^{3 x}\right) d x+2 \int\left(e^{2 x}\right) d x+\int\left(e^{x}\right) d x \\ &=\frac{e^{3 x}}{3}+e^{2 x}+e^{x}+c \\ &=\frac{e^{3 x}+e^{2 x}+e^{x}}{3}+c \\ &=\frac{1}{3}\left(e^{x}+1\right)^{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

Similar Questions

Trending Articles/News

anam-khan

CBSE extends last date for submission of LOC for Class 10, 12 board exams 2023-24
anam-khan

CBSE issues public warning against private websites asking to access practice papers
anam-khan

CBSE Board Exam 2024: Class 10, 12 private registrations begin today at cbse.gov.in

Latest Question