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 : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
`(1+ log x)^2/x`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Evaluate: `int 1/(x(x-1)) dx`
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Evaluate the following integrals : `int cos^2x.dx`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t.x:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Integrate the following functions w.r.t. x : tan5x
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
`int (logx)^2/x dx` = ______.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
`int secx/(secx - tanx)dx` equals ______.
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate `int (1)/(x(x - 1))dx`
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate `int1/(x(x-1))dx`
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Which standard substitution is used for \[\sqrt{x^2+\mathrm{a}^2}\], \[\frac{1}{\sqrt{x^2+\mathrm{a}^2}}\], or \[x^2+\mathrm{a}^2\]?
Which substitution is appropriate for \[\sqrt{\frac{\mathrm{a}-x}{\mathrm{a}+x}}\] or \[\sqrt{\frac{\mathrm{a}+x}{\mathrm{a}-x}}\]?
