Advertisements
Advertisements
Question
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
Advertisements
Solution
Let I = `int (x - 2)^2 sqrt(x)*dx`
= `int (x^2 - 4x + 4)sqrt(x)*dx`
= `int (x^(5/2) - 4x^(3/2) + 4x^(1/2))*dx`
= `int x^(5/2)*dx - 4 int x^(3/2)*dx + 4 int x^(1/2)*dx`
= `x^(7/2)/((7/2)) - 4 x^(5/2)/((5/2)) + 4 x^(3/2)/((3/2))`
= `(2)/(7)x^(7/2) - 8/5x^(5/2) + (8)/(3)x^(3/2) + c`.
APPEARS IN
RELATED QUESTIONS
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Integrate the functions:
`(log x)^2/x`
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
`e^(2x+3)`
Integrate the functions:
`cos sqrt(x)/sqrtx`
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Write a value of
Write a value of
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Write a value of\[\int \log_e x\ dx\].
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x : cos7x
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
Evaluate `int (5"x" + 1)^(4/9)` dx
Evaluate: `int "x" * "e"^"2x"` dx
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
`int 1/(xsin^2(logx)) "d"x`
`int(log(logx))/x "d"x`
`int (7x + 9)^13 "d"x` ______ + c
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
`int dx/(1 + e^-x)` = ______
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
`int sec^6 x tan x "d"x` = ______.
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
`int 1/(a^2 - x^2) dx = 1/(2a) xx` ______.
`int (f^'(x))/(f(x))dx` = ______ + c.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
If f'(x) = 4x3- 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate `int1/(x(x-1))dx`
Evaluate `int(1+x+x^2/(2!))dx`
Which substitution is appropriate for \[\sqrt{\frac{x}{a-x}}\], \[\sqrt{\frac{a-x}{x}}\], \[\sqrt{x(a-x)}\], or \[\frac{1}{\sqrt{x(a-x)}}\]?
Which expression results after simplifying \[\int\frac{\sin(t-a)}{\sin t}\,dt\]?
