Advertisements
Advertisements
Question
Choose the correct options from the given alternatives :
`int tan(sin^-1 x)*dx` =
Options
`(1 - x^2)^(-1/2) + c`
`(1 - x^2)^(1/2) + c`
`tan^m x/sqrt(1 - x^2) + c`
`- sqrt(1 - x^2) + c`
Advertisements
Solution
`-sqrt(1 - x^2) + c`
`["Hint" : sin^-1x = tan^-1 (x/sqrt(1 - x^2))].`
APPEARS IN
RELATED QUESTIONS
Integrate the function in x sin 3x.
Integrate the function in x sec2 x.
Integrate the function in `e^x (1 + sin x)/(1+cos x)`.
Integrate the function in `sin^(-1) ((2x)/(1+x^2))`.
`intx^2 e^(x^3) dx` equals:
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 x^3.tan^-1x.dx`
Evaluate the following : `int log(logx)/x.dx`
Evaluate the following : `int cos sqrt(x).dx`
Evaluate the following : `int sin θ.log (cos θ).dθ`
Evaluate the following : `int x.cos^3x.dx`
Evaluate the following: `int logx/x.dx`
Evaluate the following:
`int x.sin 2x. cos 5x.dx`
Evaluate the following : `int cos(root(3)(x)).dx`
Integrate the following functions w.r.t.x:
`e^-x cos2x`
Integrate the following functions w.r.t. x : `sqrt(5x^2 + 3)`
Integrate the following functions w.r.t. x : `sqrt(2x^2 + 3x + 4)`
Integrate the following functions w.r.t. x : `e^x .(1/x - 1/x^2)`
Integrate the following with respect to the respective variable : `(3 - 2sinx)/(cos^2x)`
Integrate the following with respect to the respective variable : cos 3x cos 2x cos x
Evaluate the following.
`int e^x (1/x - 1/x^2)`dx
Evaluate the following.
`int (log "x")/(1 + log "x")^2` dx
Evaluate: Find the primitive of `1/(1 + "e"^"x")`
`int (sin(x - "a"))/(cos (x + "b")) "d"x`
`int 1/sqrt(2x^2 - 5) "d"x`
Choose the correct alternative:
`intx^(2)3^(x^3) "d"x` =
Choose the correct alternative:
`int ("d"x)/((x - 8)(x + 7))` =
`int 1/x "d"x` = ______ + c
`int 1/(x^2 - "a"^2) "d"x` = ______ + c
Evaluate `int 1/(x(x - 1)) "d"x`
Evaluate `int 1/(4x^2 - 1) "d"x`
`int cot "x".log [log (sin "x")] "dx"` = ____________.
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
`intsqrt(1+x) dx` = ______
`int(3x^2)/sqrt(1+x^3) dx = sqrt(1+x^3)+c`
`int1/(x+sqrt(x)) dx` = ______
`inte^(xloga).e^x dx` is ______
Evaluate `int(1 + x + (x^2)/(2!))dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4))dx`
Evaluate:
`int (logx)^2 dx`
`int (sin^-1 sqrt(x) + cos^-1 sqrt(x))dx` = ______.
Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3) dx`
