Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`
Advertisements
उत्तर
Let I = `int (x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x).dx`
= `int a^(x + tan^-1x).((x^2 + 2)/(x^2 + 1)).dx`
Put x + tan–1x = t
∴ `(1 + 1/(1 + x^2)).dx` = dt
∴ `((1 + x^2 + 1)/(1 + x^2)).dx` = dt
∴ `((x^2 + 2)/(x^2 + 1)).dx` = dt
∴ I = `int a^t dt = a^t/loga + c`
= `(a^(x + tan^-1 x))/loga + c`.
APPEARS IN
संबंधित प्रश्न
Find `intsqrtx/sqrt(a^3-x^3)dx`
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
Evaluate : `∫1/(3+2sinx+cosx)dx`
Write a value of
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Evaluate the following integrals:
`int x/(x + 2).dx`
Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
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:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x : cos7x
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Choose the correct options from the given alternatives :
`int (cos2x - 1)/(cos2x + 1)*dx` =
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
`int (logx)^2/x dx` = ______.
Evaluate the following.
`int 1/(x^2 + 4x - 5) dx`
Evaluate `int(1 + x + x^2/(2!))dx`
`int x^3 e^(x^2) dx`
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
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 the following.
`intx^3/sqrt(1 + x^4)dx`
Evaluate `int1/(x(x - 1))dx`
