AP EAMCET · Maths · Indefinite Integration
\(\int \frac{1}{x^2}(2 x+1)^3 d x\) is equal to
- A \(4 x^2+12 x+6 \log x-\frac{1}{x}+C\)
- B \(4 x^2+12 x-6 \log x-\frac{2}{x}+C\)
- C \(2 x^2+8 x+3 \log x-\frac{2}{x}+C\)
- D \(8 x^2+6 x+6 \log x+\frac{2}{x}+C\)
Answer & Solution
Correct Answer
(A) \(4 x^2+12 x+6 \log x-\frac{1}{x}+C\)
Step-by-step Solution
Detailed explanation
We have, \(\int \frac{1}{x^2}(2 x+1)^3 d x\) \(\begin{aligned} & =\int \frac{\left(8 x^3+1+12 x^2+6 x\right)}{x^2} d x \\ & =\int\left(8 x+12+\frac{6}{x}+\frac{1}{z^2}\right) d x\end{aligned}\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Two dice are thrown simultaneously. If \(A\) is event of getting the sum of the numbers on two dice as greater than or equal to 8 and \(B\) is the event of getting a number less than or equal to 3 on atleast one of the die. Then, \(P(B / A)=\)AP EAMCET 2018 Easy
- In triangle \(A B C\) if \(\cos A \cos B+\sin A \sin B \sin C=1\), then \(\sin A+\sin B+\sin C=\)AP EAMCET 2025 Medium
- The number of real values of \(m\) so that the equation \(x^2+(2 m+1) x+m=0\) has equal roots isAP EAMCET 2022 Easy
- The area of the quadrilateral formed by the tangents from the point \((4,5)\) to the circle \(x^2+y^2-4 x-2 y-11=0\), with a pair of radii joining the points of contact of these tangents isAP EAMCET 2020 Hard
- In a \(\triangle A B C, \frac{a}{\tan A}+\frac{b}{\tan B}+\frac{c}{\tan C}\) is equal toAP EAMCET 2015 Medium
- If \(\alpha, \beta, \gamma\) are the roots of \(x^3+2 x+5=0\), then \(\sum \frac{\beta+\gamma}{\alpha^2}=\)AP EAMCET 2023 Medium
More PYQs from AP EAMCET
- A transverse wave propagating on a stretched string of linear density \(3 \times 10^{-4} \mathrm{~kg} \mathrm{~m}^{-1}\) is represented by the equation \(y=0.2 \sin (15 x+60 t)\)
where \(x\) is in metres and \(t\) is in seconds. The tension in the string (in newton) isAP EAMCET 2005 Hard - The outer electronic configuration of " \(\mathrm{Pd}\) " isAP EAMCET 2022 Easy
- If is such that , thenAP EAMCET 2022 Easy
- Assertion (A) The boiling points of noble gases increases from He to Xe.
Reason (R) The interatomic van der Waals' attractive forces increases from \(\mathrm{He}\) to \(\mathrm{Xe}\).
The correct answer isAP EAMCET 2012 Easy - Three faces of a fair die are yellow, two faces are red and one face is blue. If the die is tossed 3 times, then the probability that the colours yellow, red and blue appear is (need not be in that order)AP EAMCET 2017 Medium
- The probability of a non-leap year having 53 Mondays is .........AP EAMCET 2020 Easy