Advertisements
Advertisements
प्रश्न
Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Advertisements
उत्तर
Let I = `int sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Put `x^(3/2)` = t
∴ `(3)/(2) sqrt(x)*dx` = dt
∴ `sqrt(x)*dx = (2)/(3)*dt`
∴ I = `(2)/(3) int sec t tan t*dt`
= `(2)/(3)sec t + c`
= `(2)/(3) sec(x^(3/2)) + c`.
APPEARS IN
संबंधित प्रश्न
Integrate the function in x sin 3x.
Integrate the function in `x^2e^x`.
Integrate the function in `(x cos^(-1) x)/sqrt(1-x^2)`.
Integrate the function in `e^x (1 + sin x)/(1+cos x)`.
Integrate the function in e2x sin x.
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`
Evaluate the following:
`int sec^3x.dx`
Evaluate the following : `int x^3.logx.dx`
Evaluate the following : `int e^(2x).cos 3x.dx`
Evaluate the following: `int logx/x.dx`
Integrate the following functions w.r.t.x:
`e^-x cos2x`
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 : `((1 + sin x)/(1 + cos x)).e^x`
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 (1)/(cosx - cos^2x)*dx` =
Integrate the following with respect to the respective variable : `(3 - 2sinx)/(cos^2x)`
Evaluate the following.
`int "x"^3 "e"^("x"^2)`dx
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: `int "dx"/(3 - 2"x" - "x"^2)`
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
Evaluate: `int "dx"/(5 - 16"x"^2)`
Evaluate: `int "dx"/(25"x" - "x"(log "x")^2)`
`int sqrt(tanx) + sqrt(cotx) "d"x`
`int(x + 1/x)^3 dx` = ______.
Evaluate `int (2x + 1)/((x + 1)(x - 2)) "d"x`
`int "e"^x x/(x + 1)^2 "d"x`
Evaluate the following:
`int ((cos 5x + cos 4x))/(1 - 2 cos 3x) "d"x`
The value of `int_0^(pi/2) log ((4 + 3 sin x)/(4 + 3 cos x)) dx` is
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.
`int x/((x + 2)(x + 3)) dx` = ______ + `int 3/(x + 3) dx`
Evaluate: `int_0^(pi/4) (dx)/(1 + tanx)`
`int(logx)^2dx` equals ______.
If `int (f(x))/(log(sin x))dx` = log[log sin x] + c, then f(x) is equal to ______.
`int(3x^2)/sqrt(1+x^3) dx = sqrt(1+x^3)+c`
Evaluate:
`inte^x sinx dx`
`int (sin^-1 sqrt(x) + cos^-1 sqrt(x))dx` = ______.
Evaluate:
`int1/(x^2 + 25)dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate the following.
`intx^3 e^(x^2)dx`
