All Categories
Alerts
Wishlist
Cart
Sign In
Categories
Current Affairs & GK
Current Affairs
Show All Current Affairs & GK
General Aptitude
Arithmetic Aptitude
Data Interpretation
Show All General Aptitude
General Knowledge
Basic General Knowledge
General Science
Show All General Knowledge
Medical Science
Anatomy
Biochemical Engineering
Biochemistry
Biotechnology
Microbiology
Show All Medical Science
Technical
Database
Digital Electronics
Electronics
Networking
Show All Technical
Verbal and Reasoning
Logical Reasoning
Verbal Ability
Verbal Reasoning
Show All Verbal and Reasoning
›
Calculate the integral ∫ (x^2 + 2x + 1)/(x + 1) dx.
Calculate the integral ∫ (x^2 + 2x + 1)/(x + 1) dx.
Expand All
Collapse All
Practice Questions
1 question
Q1
Calculate the integral ∫ (x^2 + 2x + 1)/(x + 1) dx.
(1/3)x^3 + x^2 + C
x^2 + 2x + C
x^2 + x + C
(1/3)x^3 + (1/2)x^2 + C
Show Solution
Copy
The integrand simplifies to x + 1. Therefore, ∫ (x + 1) dx = (1/2)x^2 + x + C.
Questions & Step-by-step Solutions
1 item
Q
Q: Calculate the integral ∫ (x^2 + 2x + 1)/(x + 1) dx.
Solution:
The integrand simplifies to x + 1. Therefore, ∫ (x + 1) dx = (1/2)x^2 + x + C.
Steps: 8
Show Steps
Step 1: Start with the integral ∫ (x^2 + 2x + 1)/(x + 1) dx.
Step 2: Simplify the integrand (the expression inside the integral).
Step 3: Notice that (x^2 + 2x + 1) can be factored as (x + 1)(x + 1).
Step 4: Rewrite the integrand as ((x + 1)(x + 1))/(x + 1).
Step 5: Cancel the (x + 1) in the numerator and denominator, leaving you with x + 1.
Step 6: Now, the integral simplifies to ∫ (x + 1) dx.
Step 7: Integrate (x + 1) to find the antiderivative: ∫ (x + 1) dx = (1/2)x^2 + x + C.
Step 8: Write down the final answer: (1/2)x^2 + x + C.
Related Questions
F
Find the value of tan(45°).
Question: Find the value of tan(45°).Options: 01undefined√3Correct Answer: 1Solution: tan(45°) = 1...
W
What is the value of 5C2?
Question: What is the value of 5C2?Options: 1020155Correct Answer: 10Solution: 5C2 = 5! / (2!(5-2)!)..
W
What is the derivative of f(x) = x^3 - 3x^2 + 4x - 5?
Question: What is the derivative of f(x) = x^3 - 3x^2 + 4x - 5?Options: 3x^2 - 6x + 43x^2 - 6x2x^2 -..
F
Find the value of tan(45°) + cot(45°).
Question: Find the value of tan(45°) + cot(45°).Options: 120undefinedCorrect Answer: 2Solution: tan(..
W
What is the value of the limit lim (x -> 0) (sin(5x)/x)?
Question: What is the value of the limit lim (x -> 0) (sin(5x)/x)?Options: 01510Correct Answer: 5Sol..
‹
Biology (School & UG)
Chemistry (School & UG)
Civil Engineering
Commerce & Accountancy
Computer Science & IT
Current Affairs & GK
Data Structures & Algorithms
Electrical & Electronics Engineering
English (School)
General Aptitude
General Knowledge
General Knowledge & Current Affairs
Languages & Literature
Law & Legal Studies
Major Competitive Exams
Mathematics (School)
Mechanical Engineering
Medical Science
Physics (School & Undergraduate)
Quantitative Aptitude & Reasoning
Social Science (School)
Technical
Verbal and Reasoning
Vocational & Skill Development
›
Soulshift Feedback
×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy
?
0
1
2
3
4
5
6
7
8
9
10
Not likely
Very likely
✕
↑
