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 `int_(-pi/2)^(pi/2)sin^4x/(sin^4x+cos^4x)dx`, then the value of I is:
(A) 0
(B) π
(C) π/2
(D) π/4
Integrate the function in `x^2e^x`.
Integrate the function in x log 2x.
Integrate the function in x sec2 x.
Integrate the function in ex (sinx + cosx).
Find :
`∫(log x)^2 dx`
Evaluate the following : `int(sin(logx)^2)/x.log.x.dx`
Integrate the following functions w.r.t. x : `sqrt(2x^2 + 3x + 4)`
Integrate the following functions w.r.t. x : `log(1 + x)^((1 + x)`
Integrate the following functions w.r.t. x : cosec (log x)[1 – cot (log x)]
Choose the correct options from the given alternatives :
`int (sin^m x)/(cos^(m+2)x)*dx` =
If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = ______.
Integrate the following w.r.t.x : cot–1 (1 – x + x2)
Integrate the following w.r.t.x : `log (1 + cosx) - xtan(x/2)`
Integrate the following w.r.t.x : sec4x cosec2x
Evaluate the following.
∫ x log x dx
Evaluate the following.
`int "e"^"x" [(log "x")^2 + (2 log "x")/"x"]` dx
Evaluate: `int "dx"/(5 - 16"x"^2)`
`int (sin(x - "a"))/(cos (x + "b")) "d"x`
`int sin4x cos3x "d"x`
Choose the correct alternative:
`intx^(2)3^(x^3) "d"x` =
`int ("d"x)/(x - x^2)` = ______
`int(x + 1/x)^3 dx` = ______.
`int 1/x "d"x` = ______ + c
`int 1/sqrt(x^2 - 8x - 20) "d"x`
Evaluate the following:
`int ((cos 5x + cos 4x))/(1 - 2 cos 3x) "d"x`
`int x/((x + 2)(x + 3)) dx` = ______ + `int 3/(x + 3) dx`
Find: `int (2x)/((x^2 + 1)(x^2 + 2)) dx`
Find `int e^(cot^-1x) ((1 - x + x^2)/(1 + x^2))dx`.
Evaluate `int(3x-2)/((x+1)^2(x+3)) dx`
`inte^(xloga).e^x dx` is ______
`int logx dx = x(1+logx)+c`
Evaluate the following.
`intx^3 e^(x^2) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate:
`inte^x "cosec" x(1 - cot x)dx`
Under the LIATE rule, which type of function has priority \(L\)?
Let \[I=\int e^x\sin x\,dx.\] After applying integration by parts once, which equation is obtained?
When applying integration by parts to \(\log x\) and inverse trig, what should they be multiplied by?
