Advertisements
Advertisements
Question
Integrate the following with respect to x.
`1/(9 - 8x - x^2)`
Advertisements
Solution
`int 1/(9 - 8x - x^2) "d"x`
Consider `9 - 8x - x^2 = 3x^2 - (x^2 + 8x)`
= `9 - [(x + 4)^2 - 16]`
= `9 + 16 - (x + 4)^2`
= `25 - (x + 4)^2`
= `5^2 - (x + 4)^2`
So integral becomes
`int ("d"x)/(5^2 - (x + 4)^2) = 1/10 log|(5 + x + 4)/(5 - x - 4)| + "c"`
= `1/10 log|(9 + x)/(1 - x)| + "c"`
APPEARS IN
RELATED QUESTIONS
Integrate the following with respect to x.
`(8x + 13)/sqrt(4x + 7)`
Integrate the following with respect to x.
log x
Integrate the following with respect to x.
x8(1 + x9)5
Integrate the following with respect to x
`1/(x log x)`
Integrate the following with respect to x.
`"e"^(3x) [(3x - 1)/(9x^2)]`
Integrate the following with respect to x.
`1/sqrt(x^2 - 3x + 2)`
Choose the correct alternative:
`int 2^x "d"x` is
Choose the correct alternative:
`int (sin5x - sinx)/(cos3x) "d"x` is
Choose the correct alternative:
`int ("d"x)/sqrt(x^2 - 36) + "c"`
Choose the correct alternative:
`int (2x + 3)/sqrt(x^2 + 3x + 2) "d"x` is
