Question:
\( \int \frac{2x^2 + 4x + 3}{x^2 + x + 1} \, dx = \)
\( \int \frac{2x^2 + 4x + 3}{x^2 + x + 1} \, dx = \)
Show Hint
Always try division when numerator degree $\ge$ denominator degree.
Updated On: Apr 21, 2026
- \( 2\log_e|x^2+x+1| + C \)
- \( x\log_e|x^2+x+1| + C \)
- \( \frac{1}{2}\log_e|x^2+x+1| + C \)
- \( 2x + \log_e|x^2+x+1| + C \)
- \( x + 2\log_e|x^2+x+1| + C \)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Concept:
Split into:
\[
\frac{2x^2+4x+3}{x^2+x+1} = 2 + \frac{2x+1}{x^2+x+1}
\]
Step 1: Split integral.
\[ \int 2\,dx + \int \frac{2x+1}{x^2+x+1}dx \]
Step 2: Solve.
\[ = 2x + \log|x^2+x+1| + C \]
Step 1: Split integral.
\[ \int 2\,dx + \int \frac{2x+1}{x^2+x+1}dx \]
Step 2: Solve.
\[ = 2x + \log|x^2+x+1| + C \]
Was this answer helpful?
0
0
Top KEAM Mathematics Questions
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
- The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is
- The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is
- Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals
- Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?
View More Questions
Top KEAM integral Questions
- \(\int\frac{sin^{25}x}{cos^{27}x}dx\) is equal to
- The integral \( \int \frac{dx}{1 + e^x} \) is:
The integral \(\int e^x \sqrt{e^x} \, dx\) equals:
- The integral \( \int \frac{1 + x^2 + x^4}{(1 - x^3)(1 + x^3)} \, dx \) is equal to:
- The integral \( \int \sqrt{1 + \sin 2x} \, dx \) is equal to:
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions