Mathematics

# Integrate: $\dfrac { 3 x ^ { 2 } } { x ^ { 6 } + 1 }$

##### SOLUTION
$I=\displaystyle \int \dfrac{3x^2}{x^6 + 1} dx$

$x^3 = t$

$3x^2 dx = dt$

$I=\displaystyle \int \dfrac{3x^2}{t^2 + 1} \times \dfrac{dt}{3x^2} = \int \dfrac{dt}{t^2 + 1}$

$= \tan^{-1} (t) + c$

$= \tan^{-1} (x^3) + C$

Its FREE, you're just one step away

Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Subjective Medium
Evaluate:
$\displaystyle \int x+5 dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate the integral $\displaystyle \int_0^{\tfrac {\pi}{2}}\frac {\sin x}{1+\cos^2x}dx$   using substitution.

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\int { \dfrac { dx }{ 16{ x }^{ 2 }-25 } }$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
If $\displaystyle I = \int \cos \theta \log (\tan \theta/2) d\theta$, then I equals
• A. $\displaystyle \sin \theta \log (\tan \theta/2) + \theta + C$
• B. $\displaystyle \cos \theta \log (\tan \theta/2) + \theta + C$
• C. none of these
• D. $\displaystyle \sin \theta \log (\tan \theta/2) - \theta + C$

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.