Advertisements
Advertisements
प्रश्न
Integrate : sec3 x w. r. t. x.
Advertisements
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
If u and v are two functions of x then prove that
`intuvdx=uintvdx-int[du/dxintvdx]dx`
Hence evaluate, `int xe^xdx`
Integrate the function in `x^2e^x`.
Integrate the function in x2 log x.
Integrate the function in x cos-1 x.
Integrate the function in (x2 + 1) log x.
Integrate the function in `e^x (1/x - 1/x^2)`.
`intx^2 e^(x^3) dx` equals:
Evaluate the following : `int (t.sin^-1 t)/sqrt(1 - t^2).dt`
Evaluate the following : `int sin θ.log (cos θ).dθ`
Evaluate the following : `int(sin(logx)^2)/x.log.x.dx`
Integrate the following functions w.r.t. x : `x^2 .sqrt(a^2 - x^6)`
Integrate the following functions w.r.t. x : `xsqrt(5 - 4x - x^2)`
Integrate the following functions w.r.t. x : `e^x/x [x (logx)^2 + 2 (logx)]`
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 (log (3x))/(xlog (9x))*dx` =
Choose the correct options from the given alternatives :
`int (x- sinx)/(1 - cosx)*dx` =
Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Evaluate the following.
`int e^x (1/x - 1/x^2)`dx
Evaluate the following.
`int [1/(log "x") - 1/(log "x")^2]` dx
Choose the correct alternative from the following.
`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx"` =
Choose the correct alternative from the following.
`int (1 - "x")^(-2) "dx"` =
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
Evaluate: `int "dx"/(25"x" - "x"(log "x")^2)`
Evaluate:
∫ (log x)2 dx
`int (sinx)/(1 + sin x) "d"x`
`int logx/(1 + logx)^2 "d"x`
`int "e"^x int [(2 - sin 2x)/(1 - cos 2x)]`dx = ______.
The value of `int_0^(pi/2) log ((4 + 3 sin x)/(4 + 3 cos x)) dx` is
`int x/((x + 2)(x + 3)) dx` = ______ + `int 3/(x + 3) dx`
`int((4e^x - 25)/(2e^x - 5))dx = Ax + B log(2e^x - 5) + c`, then ______.
Find `int e^(cot^-1x) ((1 - x + x^2)/(1 + x^2))dx`.
`int1/sqrt(x^2 - a^2) dx` = ______
`intsqrt(1+x) dx` = ______
Evaluate the following.
`int x^3 e^(x^2) dx`
`int logx dx = x(1+logx)+c`
`int(xe^x)/((1+x)^2) dx` = ______
Evaluate `int tan^-1x dx`
Evaluate the following:
`intx^3e^(x^2)dx`
The value of `inta^x.e^x dx` equals
