Friday

August 22, 2014

August 22, 2014

Posted by **ZUkii** on Tuesday, May 29, 2012 at 12:39am.

(x+7)dx/x^2+14x+55

- calculus - eh? -
**Steve**, Tuesday, May 29, 2012 at 3:53ammakes no sense as written

better look again and copy it accurately

- calculus -
**Bosnian**, Tuesday, May 29, 2012 at 4:11amIf (x+7)dx/x^2+14x+55

mean

( x + 7 ) dx / ( x ^ 2 + 14 x + 55 )

then substitute :

u = x ^ 2 + 14 x + 5

d u = ( 2 x + 14 ) dx = 2 ( x + 7 ) d x Divide both sides by 2

du / 2 = ( x + 7 ) d x

( x + 7 ) d x = d u / 2

integral of [ ( x + 7 ) dx / ( x ^ 2 + 14 x + 55 ) ] =

integral of [ ( d u / 2 ) / u ) ] =

( 1 / 2 ) integral of ( du / u ) =

( 1 / 2 ) log ( u ) + C =

( 1 / 2 ) log ( x ^ 2 + 14 x + 5 ) + C =

log [ sqrt ( x ^ 2 + 14 x + 5 ) ] + C

Remark :

log is the natural logarithm

( 1 / n ) log ( a ) = log ] ( n - th root ( a ) ]

( 1 / 2 ) log ( a ) = log [ sqrt ( a ) ]

**Related Questions**

Grade 12 Calculus - Evaluate each of the following. Show all your calculations...

algebra - solve the following equation by clearing fractions show all work want ...

calculus - Evaluate the following integrals using the given substitutions. (a) (...

Calculus - Evaluate the indefinite integral. (e^7x)/(e^14x+16)dx

algebra - solve the following equation by clearing fraction want to know if this...

math - which equation is equivalent to 5x-2(7x+1)=14x? why? a -9x-2=14x b -9xt1=...

Maths - find the equation of the perpendicular bisector of the line joining P(2...

calculus - take the limit as x goes to infinity: (14x/(14x+3))^(4x)

math-calculus - 4x+3/2x-1-2 = 6x+2/2x-1 (4x+3)(-2) = (6x+2) -8x-6 = 6x+2 -14x-6...

Grade 12 Calculus - Evaluate each of the following. Show all your calculations...