Mathematics

Evaluate :$\displaystyle \int \dfrac{dx}{x(x^2+1)}$

SOLUTION
$\displaystyle I = \int \dfrac{x}{x^{2}(x^{2}+1)}dx$
let $x^{2} = t \Rightarrow 2xdx = dt$
$\Rightarrow I = \displaystyle \int \frac{dt}{2t(t+1)}(t+1-t ) = \frac{1}{2}\left [ \frac{dt}{t}-\dfrac{dt}{t+1} \right ]$
$= \dfrac{1}{2} (lnt - ln|t+1|) - \dfrac{1}{2}(ln(x^{2})-ln(1+x^{2}))+c$

Its FREE, you're just one step away

Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 111

Realted Questions

Q1 One Word Medium
$\displaystyle \int_{0}^{\pi. }\frac{dx}{1+2\sin ^{2}x}= \frac{\pi }{\sqrt{\left ( k \right )}}$
what is k?

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
$\int \dfrac{cos 2x - cos 2 \theta}{cos x - cos \theta} dx$ is equal to
• A. $2(sin x - x cos \theta) + C$
• B. $2(sin x + 2x cos \theta) + C$
• C. $2(sin x - 2x cos \theta) + C$
• D. $2(sin x + x cos \theta) + C$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
The value of $\displaystyle \int(3x^{2}\tan\frac{1}{x}-x\sec^{2}\frac{1}{x})dx {\it}$ is
• A. $x^{2}\displaystyle \tan\frac{1}{x}+c$
• B. $x\displaystyle \tan\frac{1}{x}+c$
• C. $\displaystyle \tan\frac{1}{x}+c$
• D. $x^{3}\displaystyle \tan\frac{1}{x}+c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Solve:-
$\displaystyle\int {\dfrac{1}{{\cos \lambda + \cos x}}} dx$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
The integral of $f(x) = \dfrac{1}{x\ell n x}$ is
• A. $x \ell n x + c$
• B. $\dfrac{x}{\ell n x} + c$
• C. $x + \ell n x +$
• D. $\ell n(\ell n x) + c$