Mathematics

$$\displaystyle\int \dfrac{2x^3-1}{x^4+x}dx$$ is equal to?


ANSWER

$$ln\left|\dfrac{x^3+1}{x}\right|+c$$


SOLUTION
$$\displaystyle\int \dfrac{2x^3-1}{x^4+x}dx=\displaystyle\int \dfrac{2x-x^{-2}}{x^2+x^{-1}}dx=ln(x^2+x^{-1})+c=ln(x^3+1)-lnx+c$$.
View Full Answer

Its FREE, you're just one step away


Single Correct Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84
Enroll Now For FREE

Realted Questions

Q1 Single Correct Medium
The $$p.m.f.$$ of a $$r.v.X$$ is 
$$X=x$$$$1$$$$2$$$$3$$
$$P(X=x)$$$$1/5$$$$2/5$$$$2/5$$
,then $$E(X)=$$
  • A. $$\dfrac{5}{7}$$
  • B. $$\dfrac{11}{5}$$
  • C. $$\dfrac{7}{5}$$
  • D. $$\dfrac{5}{9}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Medium
$$\displaystyle\int^{\pi}_0|\cos x|dx=?$$
  • A. $$\dfrac{3}{2}$$
  • B. $$1$$
  • C. $$0$$
  • D. $$2$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 One Word Hard
The value of $$\displaystyle \int_0^1 4x^3 \left \{ \frac{d^2}{dx^2} (1-x^2)^5 \right \} dx$$ is?

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium
$$\int_{0}^{3} (9-x^{2})^{3/2}dx_{=}$$
  • A. $$\displaystyle \frac{\pi}{16}$$
  • B. $$\displaystyle \frac{-243\pi^{2}}{15}$$
  • C. $$\displaystyle \frac{81\pi}{16}$$
  • D. $$\displaystyle \frac{243\pi}{16}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Passage Medium
Let $$n \space\epsilon \space N$$ & the A.M., G.M., H.M. & the root mean square of $$n$$ numbers $$2n+1, 2n+2, ...,$$ up to $$n^{th}$$ number are $$A_{n}$$, $$G_{n}$$, $$H_{n}$$ and $$R_{n}$$ respectively. 
On the basis of above information answer the following questions

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer