Advertisements
Advertisements
प्रश्न
Integrate : sec3 x w. r. t. x.
उत्तर
`I = intsec^3x dx`
`I =int secx.sec^2x dx`
`I =secx.intsec^2xdx-int[d/dx(secx).int sec^2x dx] dx`
`I =secx.tanx-int secx.tanx.tanx dx`
`I =secx.tanx-int secx(sec^2x -1)dx`
`I =secx.tanx-int [sec^3x-secx]dx`
`I =secx.tanx-int sec^3x + int secxdx`
`I =secx.tanx - I + log|secx + tanx| + c`
`2I =secx.tanx + log|secx + tanx| + c`
`therefore I =1/2(secx.tanx + log|secx + tanx|) + c`
APPEARS IN
संबंधित प्रश्न
Integrate the function in x sin x.
Integrate the function in x2 log x.
Integrate the function in x cos-1 x.
Integrate the function in (sin-1x)2.
Integrate the function in x sec2 x.
Integrate the function in tan-1 x.
Integrate the function in ex (sinx + cosx).
Integrate the function in `sin^(-1) ((2x)/(1+x^2))`.
`intx^2 e^(x^3) dx` equals:
Prove that:
`int sqrt(x^2 + a^2)dx = x/2 sqrt(x^2 + a^2) + a^2/2 log |x + sqrt(x^2 + a^2)| + c`
Find :
`∫(log x)^2 dx`
Evaluate the following : `int x^2 sin 3x dx`
Evaluate the following : `int (t.sin^-1 t)/sqrt(1 - t^2).dt`
Evaluate the following : `int(sin(logx)^2)/x.log.x.dx`
Integrate the following functions w.r.t. x : `e^(2x).sin3x`
Integrate the following functions w.r.t. x:
sin (log x)
Integrate the following functions w.r.t. x : `sqrt((x - 3)(7 - x)`
Integrate the following functions w.r.t. x : `sec^2x.sqrt(tan^2x + tan x - 7)`
Integrate the following functions w.r.t. x : `sqrt(x^2 + 2x + 5)`
Integrate the following functions w.r.t. x : `e^(sin^-1x)*[(x + sqrt(1 - x^2))/sqrt(1 - x^2)]`
Integrate the following functions w.r.t. x : cosec (log x)[1 – cot (log x)]
If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(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: `(1 + log x)^2/x`
Integrate the following w.r.t.x : cot–1 (1 – x + x2)
Integrate the following w.r.t.x : `(1)/(x^3 sqrt(x^2 - 1)`
Integrate the following w.r.t.x : e2x sin x cos x
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 "e"^"x" (1/"x" - 1/"x"^2)`dx
Evaluate the following.
`int "e"^"x" "x - 1"/("x + 1")^3` dx
Evaluate the following.
`int "e"^"x" [(log "x")^2 + (2 log "x")/"x"]` dx
Evaluate the following.
`int [1/(log "x") - 1/(log "x")^2]` dx
Evaluate: `int "dx"/(3 - 2"x" - "x"^2)`
Evaluate: `int "dx"/("x"[(log "x")^2 + 4 log "x" - 1])`
Evaluate: `int "dx"/(25"x" - "x"(log "x")^2)`
`int 1/(4x + 5x^(-11)) "d"x`
`int (sin(x - "a"))/(cos (x + "b")) "d"x`
`int (cos2x)/(sin^2x cos^2x) "d"x`
`int ("e"^xlog(sin"e"^x))/(tan"e"^x) "d"x`
Choose the correct alternative:
`intx^(2)3^(x^3) "d"x` =
`int(x + 1/x)^3 dx` = ______.
`int"e"^(4x - 3) "d"x` = ______ + c
Evaluate `int (2x + 1)/((x + 1)(x - 2)) "d"x`
`int "e"^x x/(x + 1)^2 "d"x`
`int 1/sqrt(x^2 - 8x - 20) "d"x`
The value of `int "e"^(5x) (1/x - 1/(5x^2)) "d"x` is ______.
`int tan^-1 sqrt(x) "d"x` is equal to ______.
If u and v ore differentiable functions of x. then prove that:
`int uv dx = u intv dx - int [(du)/(d) intv dx]dx`
Hence evaluate `intlog x dx`
State whether the following statement is true or false.
If `int (4e^x - 25)/(2e^x - 5)` dx = Ax – 3 log |2ex – 5| + c, where c is the constant of integration, then A = 5.
Find the general solution of the differential equation: `e^((dy)/(dx)) = x^2`.
Solve: `int sqrt(4x^2 + 5)dx`
`int(logx)^2dx` equals ______.
If `int(2e^(5x) + e^(4x) - 4e^(3x) + 4e^(2x) + 2e^x)/((e^(2x) + 4)(e^(2x) - 1)^2)dx = tan^-1(e^x/a) - 1/(b(e^(2x) - 1)) + C`, where C is constant of integration, then value of a + b is equal to ______.
If `π/2` < x < π, then `intxsqrt((1 + cos2x)/2)dx` = ______.
`int((4e^x - 25)/(2e^x - 5))dx = Ax + B log(2e^x - 5) + c`, then ______.
Find `int (sin^-1x)/(1 - x^2)^(3//2) dx`.
`int1/(x+sqrt(x)) dx` = ______
The integrating factor of `ylogy.dx/dy+x-logy=0` is ______.
`int(xe^x)/((1+x)^2) dx` = ______
Evaluate `int(1 + x + (x^2)/(2!))dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4))dx`
Evaluate:
`int1/(x^2 + 25)dx`
Evaluate the following:
`intx^3e^(x^2)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).
Evaluate:
`int x^2 cos x dx`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate the following.
`intx^2e^(4x)dx`
