Advertisements
Advertisements
प्रश्न
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Advertisements
उत्तर
Let I = `int (3"x"^3 - 2sqrt"x")/"x"` dx
`= int ("3x"^3/"x" - "2x"^(1/2)/"x")` dx
`= int (3"x"^2 - 2"x"^(-1/2))` dx
`= 3 int "x"^2 * "dx" - 2 int "x"^(-1/2) * "dx"`
`= 3 ("x"^3/3) - 2("x"^(1/2)/(1/2))` + c
∴ I = x3 - 4`sqrt"x"` + c
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Evaluate the following integrals : `int sqrt((9 - x)/x).dx`
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Fill in the Blank.
`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
State whether the following statement is True or False.
If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
`int secx/(secx - tanx)dx` equals ______.
Evaluate `int 1/(x(x-1))dx`
