Compute the integral show all work please. x +1(b)dx. (Hint: start by completing squares.)J Va² + 10x + 28

given∫x+1x2+10x+28dxlet us write numeratorAddx(x2+10x+28)+B=x+1A(2x+10)+B=x+12Ax+10A+B=x+1comparing…

Answered: x +1 dx. Vx² + 10x + 28

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter12: Quadratic Functions

Section12.4: Graphs Of Quadratic Equations: The Discriminant

Problem 7OE

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Compute the integral show all work please.

x +1
(b)
dx. (Hint: start by completing squares.)
J Va² + 10x + 28

Expert Solution

Step 1

$g i v e n \int \frac{x + 1}{\sqrt{x^{2} + 10 x + 28}} d x l e t u s w r i t e n u m e r a t o r A \frac{d}{d x} (x^{2} + 10 x + 28) + B = x + 1 A (2 x + 10) + B = x + 1 2 A x + 10 A + B = x + 1 c o m p a r i n g c o e f f i c i e n t s 2 A = 1 A = \frac{1}{2} 10 A + B = 1 10 (\frac{1}{2}) + B = 1 B = - 4 t h e r e f o r e \frac{1}{2} (2 x + 10) - 4 = x + 1$

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