Posted by ZUkii on Tuesday, May 29, 2012 at 12:39am.
makes no sense as written
better look again and copy it accurately
If (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
Calculus - Evaluate the indefinite integral. (e^7x)/(e^14x+16)dx
Calculus - I am having trouble with these 2 problems. Evaluate: (1/x^9)dx ...
calculus - Calculus A, Evaluate the following integral : ç (x^2+3x-...
calculus - Use the fundamental theorem of calculus to evaluate the following ...
calculus - Evaluate the following integral: (X)(cube root(x+1))dx
Calculus - Evaluate the following integral integral 1 = a and b = 4 of sinx dx/(...
calculus - Find or evaluate the following integral. csc^2 3x dx
Calculus - "Evaluate the following indefinite integral using integration by...
Calculus - Evaluate the integral: 16csc(x) dx from pi/2 to pi (and determine if ...
calculus - Evaluate the following integrals by using appropriate method : &#...
For Further Reading
