Advertisements
Advertisements
Question
Integrate the following with respect to x.
x8(1 + x9)5
Advertisements
Solution
Let f(x) = 1 + x9
Then f'(x) = 9x8
So `int x^8 (1 + x^9)^5 "d"x = 1/9 int 9x^8(1 + x^9)^5 "d"x`
= `1/9 int ["f"(x)]^5 "f'"(x) "d"x`
= `1/9 ["f"(x)]^6/6 + "c"`
= `1/54 (1 + x^9)^6 + "c"`
APPEARS IN
RELATED QUESTIONS
Integrate the following with respect to x.
If f'(x) = x + b, f(1) = 5 and f(2) = 13, then find f(x)
Integrate the following with respect to x.
2 cos x – 3 sin x + 4 sec2x – 5 cosec2x
Integrate the following with respect to x.
`(cos 2x + 2sin^2x)/(cos^2x)`
Integrate the following with respect to x.
`(log x)^3/x`
Integrate the following with respect to x.
`1/(9 - 8x - x^2)`
Integrate the following with respect to x.
`sqrt(1 + x + x^2)`
Choose the correct alternative:
`int (sin2x)/(2sinx) "d"x` is
Choose the correct alternative:
`int_0^4 (sqrt(x) + 1/sqrt(x)) "d"x` is
Choose the correct alternative:
`int_0^(pi/3) tan x "d"x` is
Evaluate the following integral:
`int 1/(sqrt(x + 2) - sqrt(x + 3)) "d"x`
