Mathematics

Solve $$\displaystyle\int {\dfrac{{{x^5}}}{{{x^2} + 1}}} dx $$


ANSWER

$$\dfrac{{{x^4}}}{4} - \dfrac{{{x^2}}}{2} + \dfrac{1}{2}\log \left( {{x^2} + 1} \right) + c$$


SOLUTION

Consider the given integral.

$$I=\int{\dfrac{{{x}^{5}}}{{{x}^{2}}+1}}dx$$

$$ I=\int{\left( {{x}^{3}}-x+\dfrac{x}{{{x}^{2}}+1} \right)}dx $$

$$ I=\int{\left( {{x}^{3}}-x+\dfrac{1}{2}\left( \dfrac{2x}{{{x}^{2}}+1} \right) \right)}dx $$

$$ I=\dfrac{{{x}^{4}}}{4}-\dfrac{{{x}^{2}}}{2}+\dfrac{1}{2}{{\log }_{e}}\left( {{x}^{2}}+1 \right)+C $$

 

Hence, this is the answer.

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 Subjective Medium
Integrate the function    $$\cfrac {5x}{(x+1)(x^2+9)}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Medium
Evaluate $$\displaystyle\int_{0}^{6}(x+2)\ dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Medium
$$n\overset{Lt}{\rightarrow}\infty \displaystyle \frac{1}{n}\{\sin^{2}\frac{\pi}{2n}+\sin^{2}\frac{2\pi}{2n}+\ldots+\sin^{2}\frac{n\pi}{2n}\}=$$
  • A.
  • B. 1
  • C. 2
  • D. 1/2

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Subjective Hard
Integrate:
$$\displaystyle\int{1 \over {\sqrt {(x - a)(x - b)} }}dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Easy
$$\int \frac{2x^{2}}{3x^{4}2x} dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer