Find the following integral: int frac{d x}{x^ | vedclass

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

Question

(A) We have $x^{2}-6 x+13 = x^{2}-6 x+9-9+13 = (x-3)^{2}+4 = (x-3)^{2}+2^{2}$.So,$\int \frac{d x}{x^{2}-6 x+13} = \int \frac{d x}{(x-3)^{2}+2^{2}}$.Le

Vedclass · Accepted Answer

$\frac{1}{2} 	an^{-1} \left( \frac{x-3}{2} ight) + C$

Vedclass · Answer

(A) We have $x^{2}-6 x+13 = x^{2}-6 x+9-9+13 = (x-3)^{2}+4 = (x-3)^{2}+2^{2}$.So,$\int \frac{d x}{x^{2}-6 x+13} = \int \frac{d x}{(x-3)^{2}+2^{2}}$.Let $x-3 = t$. Then $dx = dt$.Using the standard integral formula $\int \frac{dx}{x^{2}+a^{2}} = \frac{1}{a} 	an^{-1} \left( \frac{x}{a} ight) + C$,we get:$\int \frac{dt}{t^{2}+2^{2}} = \frac{1}{2} 	an^{-1} \left( \frac{t}{2} ight) + C$.Substituting $t = x-3$ back,we get:$= \frac{1}{2} 	an^{-1} \left( \frac{x-3}{2} ight) + C$.

Find the following integral: $\int \frac{d x}{x^{2}-6 x+13}$

Similar Questions

Find the integral of the function $\cos 2x \cos 4x \cos 6x$.

Find an anti-derivative for the following function using the method of inspection:
$\cos 2x$

$\text{If } \int \frac{3x+2}{4x^2+4x+5} dx = A \log(4x^2+4x+5) + B \tan^{-1}\left(x+\frac{1}{2}\right) + C, \text{ then } (A, B) = $

$\int \frac{x^8-9 x^2+18}{x^4-3 x^2+3} d x=$

Find the following integral: $\int \sqrt{x}(3x^{2} + 2x + 3) dx$

Vedclass Test Series

Exam Paper Generator

Online Exam Module