int frac{dx}{sqrt{7-6x-x^2}} is equal to | vedclass

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

Question

(C) Let $I = \int \frac{dx}{\sqrt{7-6x-x^2}}$.First,complete the square for the quadratic expression $7-6x-x^2$:$7-6x-x^2 = 7 - (x^2 + 6x) = 7 - (x^2

Vedclass · Accepted Answer

$\sin^{-1}\left(\frac{x+3}{4}\right)+C$

Vedclass · Answer

(C) Let $I = \int \frac{dx}{\sqrt{7-6x-x^2}}$.First,complete the square for the quadratic expression $7-6x-x^2$:$7-6x-x^2 = 7 - (x^2 + 6x) = 7 - (x^2 + 6x + 9 - 9) = 7 - ((x+3)^2 - 9) = 16 - (x+3)^2 = 4^2 - (x+3)^2$.Now,substitute this into the integral:$I = \int \frac{dx}{\sqrt{4^2 - (x+3)^2}}$.Using the standard integral formula $\int \frac{dx}{\sqrt{a^2 - x^2}} = \sin^{-1}\left(\frac{x}{a}\right) + C$,where $a = 4$ and $x$ is replaced by $(x+3)$:$I = \sin^{-1}\left(\frac{x+3}{4}\right) + C$.

$\int \frac{dx}{\sqrt{7-6x-x^2}}$ is equal to

Similar Questions

If $\int \sqrt{2} \sqrt{1 + \sin x} \, dx = -4 \cos(ax + b) + c$,then the value of $(a, b)$ is

$\int \frac{dx}{\sin x + \sqrt{3} \cos x} = $

If $f\left( \frac{x - 4}{x + 2} \right) = 2x + 1$ for $x \in R \setminus \{ -2 \}$,then $\int f(x) \,dx$ is equal to (where $C$ is a constant of integration)

$\int \frac{x^4+x^2+1}{x^2-x+1} \,d x$ is equal to

If $\int \frac{e^x-1}{e^x+1} dx = f(x) + c$,then $f(x)$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module