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
`int1/xlogxdx=...............`
(A)log(log x)+ c
(B) 1/2 (logx )2+c
(C) 2log x + c
(D) log x + c
Integrate the function in `x^2e^x`.
Integrate the function in x2 log x.
Integrate the function in x tan-1 x.
Integrate the function in (x2 + 1) log x.
Integrate the function in `(xe^x)/(1+x)^2`.
Integrate the function in `e^x (1/x - 1/x^2)`.
Evaluate the following : `int x^2.log x.dx`
Evaluate the following:
`int sec^3x.dx`
Evaluate the following : `int log(logx)/x.dx`
Evaluate the following : `int (t.sin^-1 t)/sqrt(1 - t^2).dt`
Integrate the following functions w.r.t. x : `(x + 1) sqrt(2x^2 + 3)`
Integrate the following functions w.r.t. x : `e^x .(1/x - 1/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 tan(sin^-1 x)*dx` =
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 cos -(3)/(7)x*sin -(11)/(7)x*dx` =
Integrate the following with respect to the respective variable : `t^3/(t + 1)^2`
Integrate the following w.r.t.x : cot–1 (1 – x + x2)
Integrate the following w.r.t.x : sec4x cosec2x
Solve the following differential equation.
(x2 − yx2 ) dy + (y2 + xy2) dx = 0
Evaluate the following.
∫ x log x dx
Evaluate the following.
`int x^2 *e^(3x)`dx
Choose the correct alternative from the following.
`int (1 - "x")^(-2) "dx"` =
Choose the correct alternative from the following.
`int (("x"^3 + 3"x"^2 + 3"x" + 1))/("x + 1")^5 "dx"` =
Evaluate: `int "dx"/(3 - 2"x" - "x"^2)`
`int (sin(x - "a"))/(cos (x + "b")) "d"x`
Evaluate `int 1/(4x^2 - 1) "d"x`
`int [(log x - 1)/(1 + (log x)^2)]^2`dx = ?
`int "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.
`int "e"^x int [(2 - sin 2x)/(1 - cos 2x)]`dx = ______.
Evaluate the following:
`int ((cos 5x + cos 4x))/(1 - 2 cos 3x) "d"x`
`int 1/sqrt(x^2 - 9) dx` = ______.
`int1/sqrt(x^2 - a^2) dx` = ______
`int(3x^2)/sqrt(1+x^3) dx = sqrt(1+x^3)+c`
`int(xe^x)/((1+x)^2) dx` = ______
Solve the following
`int_0^1 e^(x^2) x^3 dx`
If u and v are two differentiable functions of x, then prove that `intu*v*dx = u*intv dx - int(d/dx u)(intv dx)dx`. Hence evaluate: `intx cos x dx`
Evaluate:
`int1/(x^2 + 25)dx`
Evaluate `int (1 + x + x^2/(2!))dx`
Which pair is listed as Trigonometric in the LIATE rule?
Which pair is listed as Exponential in the LIATE rule?
For \[\int \frac{x\sin^{-1}x}{\sqrt{1-x^2}}\,dx,\] which functions are chosen as the first function and the second function?
Which substitution can also be used before integrating by parts for \[\int \frac{x\sin^{-1}x}{\sqrt{1-x^2}}\,dx?\]
