Advertisements
Advertisements
प्रश्न
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
उत्तर
`int(3x^3 - 2x + 5)/(xsqrt(x))dx`
= `intx^((-3)/(2))(3x^3 - 2x + 5)dx`
= `int(3x^(3/2) - 2x^(-1/2) + 5x^(-3/2))dx`
= `3intx^(3/2)dx - 2intx^(-1/2) dx + 5int x^(-3/2)dx`
= `3(x^(3/2 + 1)/(3/2 + 1)) - 2(x^(1/2 + 1)/(-1/2 + 1)) + 5(x^(-3/2 + 1)/(-3/2 + 1)) + c`
= `(6)/(5)x^2sqrt(x) - 4sqrt(x) - (10)/sqrt(x) + c`.
APPEARS IN
संबंधित प्रश्न
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
`cos sqrt(x)/sqrtx`
Integrate the functions:
`(1+ log x)^2/x`
Write a value of
Write a value of
Write a value of
Write a value of\[\int \log_e x\ dx\].
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals : `int sin 4x cos 3x dx`
Evaluate the following integrals : `int cos^2x.dx`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Integrate the following functions w.r.t. x : `(3e^(2x) + 5)/(4e^(2x) - 5)`
Integrate the following functions w.r.t. x : sin5x.cos8x
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
Evaluate the following : `int (logx)2.dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Integrate the following w.r.t.x : `(3x + 1)/sqrt(-2x^2 + x + 3)`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate `int 1/("x" ("x" - 1))` dx
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Fill in the Blank.
To find the value of `int ((1 + log "x") "dx")/"x"` the proper substitution is ________
Fill in the Blank.
`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______
Evaluate: `int "x" * "e"^"2x"` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
`int(log(logx))/x "d"x`
Choose the correct alternative:
`int(1 - x)^(-2) dx` = ______.
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
`int x^3"e"^(x^2) "d"x`
`int (1 + x)/(x + "e"^(-x)) "d"x`
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
The value of `intsinx/(sinx - cosx)dx` equals ______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
if `f(x) = 4x^3 - 3x^2 + 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 the following
`int1/(x^2 +4x-5)dx`
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
