int frac{d x}{x^2+2 x+5} = . . . . . . + C | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) To evaluate the integral $I = \int \frac{d x}{x^2+2 x+5}$,we first complete the square in the denominator.$x^2 + 2x + 5 = (x^2 + 2x + 1) + 4 = (x+

Vedclass · Accepted Answer

$\frac{1}{2} 	an ^{-1}\left(\frac{x+1}{2}ight)$

Vedclass · Answer

(B) To evaluate the integral $I = \int \frac{d x}{x^2+2 x+5}$,we first complete the square in the denominator.$x^2 + 2x + 5 = (x^2 + 2x + 1) + 4 = (x+1)^2 + 2^2$.Now,the integral becomes $I = \int \frac{d x}{(x+1)^2 + 2^2}$.Using the standard integration formula $\int \frac{dx}{x^2 + a^2} = \frac{1}{a} 	an^{-1}(\frac{x}{a}) + C$,where $a = 2$ and the variable is $(x+1)$:$I = \frac{1}{2} 	an^{-1}\left(\frac{x+1}{2}ight) + C$.Comparing this with the given options,the correct option is $B$.

$\int \frac{d x}{x^2+2 x+5} = $ . . . . . . $+ C$.

Similar Questions

If $f\left(\frac{2 x+3}{3 x+5}\right)=x+4$, where $x \neq \frac{-5}{3}, \frac{-2}{3}$, and $\int f(x) d x=A x+B \ln |3 x-2|+C$, then $3 B-A=$

The value of $\int \frac{d x}{7+6 x-x^2}$ is equal to

If $\int x^{x}(1+\log x) d x=k x^{x}+c$,then $k=$

$\int {(\sin^4 x - \cos^4 x) \, dx} = $

If $\int f(x) dx = g(x)$,then $\int f(x) g(x) dx$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module