Advertisements
Advertisements
प्रश्न
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Advertisements
उत्तर
`int (2x - 7)/sqrt(4x - 1).dx`
= `(1)/(2)int(2(2x - 7))/sqrt(4x - 1).dx`
= `(1)/(2)int((4x - 1) - 13)/sqrt(4x - 1).dx`
= `(1)/(2)int(((4x - 1))/sqrt(4x - 1) - 13/sqrt(4x - 1)).dx`
= `(1)/(2)int (4x - 1)^(1/2).dx - 13/2 int(4x - 1)^(-1/2).dx`
= `(1)/(2)((4x - 1)^(3/2))/((4)(3/2)) - (13)/(2).((4x - 1)^(1/2))/((4)(1/2)) + c`
= `(1)/(12)(4x - 1)^(3/2) - (13)/(4)sqrt(4x - 1) + c`
संबंधित प्रश्न
Evaluate :`intxlogxdx`
Integrate the functions:
`(log x)^2/x`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Write a value of
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
Evaluate the following integrals:
tan2x dx
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(x^2)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Integrate the following functions w.r.t. x : cos7x
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
If f'(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int 1/("x" log "x")`dx
Evaluate the following.
`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt
`int sqrt(1 + "x"^2) "dx"` =
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
`int(1 - x)^(-2) dx` = ______.
`int(log(logx) + 1/(logx)^2)dx` = ______.
If `int sinx/(sin^3x + cos^3x)dx = α log_e |1 + tan x| + β log_e |1 - tan x + tan^2x| + γ tan^-1 ((2tanx - 1)/sqrt(3)) + C`, when C is constant of integration, then the value of 18(α + β + γ2) is ______.
Find `int dx/sqrt(sin^3x cos(x - α))`.
`int secx/(secx - tanx)dx` equals ______.
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
