Mathematics

Prove that
$$\displaystyle \int \dfrac {x^{2}}{x^{6}+1}dx$$


SOLUTION
We have,
$$\begin{array}{l} \int { \dfrac { { { x^{ 2 } } } }{ { { x^{ 6 } }+1 } }  } dx \\ put\, \, \, { x^{ 3 } }=t\, \, \, 3{ x^{ 2 } }dx=dt \\ =\int { \dfrac { { \dfrac { { dt } }{ 3 }  } }{ { { t^{ 2 } }+1 } }  }  \\ =\dfrac { 1 }{ 3 } { \tan ^{ -1 }  }t+c \\ =\dfrac { 1 }{ 3 } { \tan ^{ -1 }  }{ x^{ 3 } }+c \end{array}$$

Hence, this is the answer.
View Full Answer

Its FREE, you're just one step away


Subjective 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
Find  $$ \int { \dfrac { ({ x }^{ 2 }+1)({ { x }^{ 2 } }+2) }{ ({ { x }^{ 2 } }+3)({ { x }^{ 2 } }+4) } dx }$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Medium
$$\displaystyle \int \dfrac{x^4}{1+x^2}dx =$$
  • A. $$\dfrac{x^2}{2}- tan^{-1} x+c$$
  • B. $$x - tan^{-1} x+c$$
  • C. None of these
  • D. $$\dfrac{x^3}{3}- x+ tan^{-1} x+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Hard

$$\displaystyle \int_{0}^{\pi /2}\frac{\sin^{2}x}{\sin x+\cos x}dx=$$
  • A. $$\sqrt{2}\log(\sqrt{2}+1)$$
  • B. $$\log(\sqrt{2}+1)$$
  • C. $$\displaystyle \frac{1}{\sqrt{2}}\log(\sqrt{2}-1)$$
  • D. $$\displaystyle \frac{1}{\sqrt{2}}l\mathrm{o}\mathrm{g}(\sqrt{2}+1)$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Subjective Medium
Evaluate $$\displaystyle\int^2_1\dfrac{dx}{x(1+2x)^2}$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Easy
Evaluate $$\int \dfrac{e^x-e^{-x}}{e^x+e^{-x}}dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer