Advertisements
Advertisements
प्रश्न
If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = ______.
पर्याय
`e^(sin^-1x)*(sin^-1 x - 1) + c`
`e^(sin^-1x)*(1 - sin^-1x) + c`
`e^(sin^-1x)*(sin^-1 x + 1) + c`
`-e^(sin^-1x)*(sin^-1 x + 1) + c`
Advertisements
उत्तर
If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = `underlinebb(e^(sin^-1x)*(sin^-1 x - 1) + c)`.
संबंधित प्रश्न
Integrate the function in `x^2e^x`.
Integrate the function in `(x cos^(-1) x)/sqrt(1-x^2)`.
Integrate the function in ex (sinx + cosx).
Integrate the function in `(xe^x)/(1+x)^2`.
`int e^x sec x (1 + tan x) dx` equals:
Evaluate the following:
`int x tan^-1 x . dx`
Integrate the following functions w.r.t. x : `sqrt(4^x(4^x + 4))`
Integrate the following functions w.r.t. x : `xsqrt(5 - 4x - x^2)`
Integrate the following functions w.r.t. x: `sqrt(x^2 + 2x + 5)`.
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)`
Choose the correct options from the given alternatives :
`int [sin (log x) + cos (log x)]*dx` =
Integrate the following with respect to the respective variable : `(sin^6θ + cos^6θ)/(sin^2θ*cos^2θ)`
Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Integrate the following w.r.t.x : sec4x cosec2x
Evaluate the following.
`int x^3 e^(x^2)`dx
Evaluate the following.
`int e^x (1/x - 1/x^2)`dx
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
`int 1/(4x + 5x^(-11)) "d"x`
`int (sin(x - "a"))/(cos (x + "b")) "d"x`
`int 1/sqrt(2x^2 - 5) "d"x`
`int (cos2x)/(sin^2x cos^2x) "d"x`
`int ("d"x)/(x - x^2)` = ______
`int 1/x "d"x` = ______ + c
`int "e"^x x/(x + 1)^2 "d"x`
`int logx/(1 + logx)^2 "d"x`
`int [(log x - 1)/(1 + (log x)^2)]^2`dx = ?
`int log x * [log ("e"x)]^-2` dx = ?
Find `int_0^1 x(tan^-1x) "d"x`
Evaluate the following:
`int_0^1 x log(1 + 2x) "d"x`
`int 1/sqrt(x^2 - 9) 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: `int e^x.sin2xdx`
`int 1/sqrt(x^2 - a^2)dx` = ______.
Solve: `int sqrt(4x^2 + 5)dx`
`int_0^1 x tan^-1 x dx` = ______.
`int((4e^x - 25)/(2e^x - 5))dx = Ax + B log(2e^x - 5) + c`, then ______.
`int(1-x)^-2 dx` = ______
`int1/sqrt(x^2 - a^2) dx` = ______
Evaluate `int(1 + x + (x^2)/(2!))dx`
Evaluate:
`int e^(logcosx)dx`
The value of `int e^x((1 + sinx)/(1 + cosx))dx` is ______.
Evaluate the following.
`intx^3/sqrt(1+x^4) dx`
The value of `int (x sin^-1)/(sqrt(1 - x^2)) dx` is equal to:
If \(u\) and \(v\) are differentiable functions, which formula is used for integration by parts?
Which function is an example under priority \(I\) in the LIATE rule?
Evaluate \[\int x\cos x\,dx.\]
Which differentiation identity verifies the special integral \[\int e^x\left[f(x)+f'(x)\right]dx=e^xf(x)+C?\]
