Advertisements
Advertisements
प्रश्न
Integrate the following with respect to the respective variable : `(3 - 2sinx)/(cos^2x)`
Advertisements
उत्तर
Let I = `int (3- 2sinx)/(cos^2x)*dx`
= `int(3/(cos^2x) - (2sinx)/(cos^2x))*dx`
= `3 int sec^2x*dx - 2int sec x tanx*dx`
= 3 tan x – 2 sec x + c.
APPEARS IN
संबंधित प्रश्न
Integrate : sec3 x w. r. t. x.
Integrate the function in x2 log x.
Integrate the function in x cos-1 x.
Integrate the function in `(xe^x)/(1+x)^2`.
Evaluate the following: `int x.sin^-1 x.dx`
Evaluate the following : `int cos sqrt(x).dx`
Evaluate the following: `int logx/x.dx`
Evaluate the following : `int cos(root(3)(x)).dx`
Integrate the following functions w.r.t. x:
sin (log x)
Integrate the following functions w.r.t. x : `sqrt(5x^2 + 3)`
Integrate the following functions w.r.t. x : `x^2 .sqrt(a^2 - x^6)`
Integrate the following functions w.r.t. x : `sec^2x.sqrt(tan^2x + tan x - 7)`
Integrate the following functions w.r.t. x : [2 + cot x – cosec2x]ex
Choose the correct options from the given alternatives :
`int (1)/(x + x^5)*dx` = f(x) + c, then `int x^4/(x + x^5)*dx` =
Choose the correct options from the given alternatives :
`int tan(sin^-1 x)*dx` =
Choose the correct options from the given alternatives :
`int [sin (log x) + cos (log x)]*dx` =
Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Integrate the following w.r.t.x : `(1)/(x^3 sqrt(x^2 - 1)`
Integrate the following w.r.t.x : sec4x cosec2x
Solve the following differential equation.
(x2 − yx2 ) dy + (y2 + xy2) dx = 0
Evaluate the following.
`int x^2 e^4x`dx
Evaluate the following.
`int (log "x")/(1 + log "x")^2` dx
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
Choose the correct alternative:
`intx^(2)3^(x^3) "d"x` =
`int ("d"x)/(x - x^2)` = ______
`int 1/(x^2 - "a"^2) "d"x` = ______ + c
`int (x^2 + x - 6)/((x - 2)(x - 1)) "d"x` = x + ______ + c
Find `int_0^1 x(tan^-1x) "d"x`
`int tan^-1 sqrt(x) "d"x` is equal to ______.
`int 1/sqrt(x^2 - 9) dx` = ______.
`int x/((x + 2)(x + 3)) dx` = ______ + `int 3/(x + 3) dx`
Find the general solution of the differential equation: `e^((dy)/(dx)) = x^2`.
If `int(x + (cos^-1 3x)^2)/sqrt(1 - 9x^2)dx = 1/α(sqrt(1 - 9x^2) + (cos^-1 3x)^β) + C`, where C is constant of integration , then (α + 3β) is equal to ______.
`int1/sqrt(x^2 - a^2) dx` = ______
`intsqrt(1+x) dx` = ______
`int logx dx = x(1+logx)+c`
`int(xe^x)/((1+x)^2) dx` = ______
Evaluate:
`int((1 + sinx)/(1 + cosx))e^x dx`
Evaluate:
`int e^(logcosx)dx`
`int (sin^-1 sqrt(x) + cos^-1 sqrt(x))dx` = ______.
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`intx^3 e^(x^2) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4) dx`
The value of `inta^x.e^x dx` equals
Evaluate `int(1 + x + x^2/(2!))dx`.
The value of `int (x sin^-1)/(sqrt(1 - x^2)) dx` is equal to:
Integration by parts is a method of integration based on which rule of differentiation?
Let \[I=\int e^x\sin x\,dx.\] After applying integration by parts once, which equation is obtained?
