Advertisements
Advertisements
Question
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Solution
Let I = ∫ (x + 1)(x + 2)7 (x + 3)dx
Put x + 2 = t
∴ dx = dt
Also, x = t - 2
∴ x + 1 = t - 2 + 1
= t - 1
and x + 3 = t - 2 + 3
= t + 1
∴ I = `int ("t" - 1) * "t"^7 ("t" + 1) * "dt"`
`= int ("t"^2 - 1) * "t"^7 * "dt"`
`= int ("t"^9 - "t"^7) "dt"`
`= int "t"^9 "dt" - int "t"^7 "dt"`
`= "t"^10/10 - "t"^8/8 + "c"`
∴ I = `("x + 2")^10/10 - ("x + 2")^8/8` + c
APPEARS IN
RELATED QUESTIONS
Integrate the functions:
`x/(e^(x^2))`
Integrate the functions:
cot x log sin x
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Integrate the following functions w.r.t. x : `(2x + 1)sqrt(x + 2)`
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
`int 1/(cos x - sin x)` dx = _______________
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
Evaluate `int1/(x(x-1))dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
