Advertisements
Advertisements
Question
`int x^2/sqrt(1 - x^6)` dx = ________________
Options
−sin−1 (x3) + c
cos−1 (x3) + c
sin−1 (x3) + c
`1/3 sin^(-1) (x^3) + "c"`
Advertisements
Solution
`1/3 sin^(-1) (x^3) + "c"`
APPEARS IN
RELATED QUESTIONS
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`xsqrt(x + 2)`
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
cot x log sin x
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Integrate the functions:
`(1+ log x)^2/x`
Write a value of
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
State whether the following statement is True or False.
If `int x "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.
Evaluate: ∫ |x| dx if x < 0
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int sqrt(1 + sin2x) dx`
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
`int1/(4 + 3cos^2x)dx` = ______
`int ("d"x)/(x(x^4 + 1))` = ______.
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
`int 1/(a^2 - x^2) dx = 1/(2a) xx` ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
`int x/sqrt(1 - 2x^4) dx` = ______.
(where c is a constant of integration)
Evaluate `int(1+ x + x^2/(2!)) dx`
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Which substitution is appropriate for \[\sqrt{\frac{\mathrm{a}-x}{\mathrm{a}+x}}\] or \[\sqrt{\frac{\mathrm{a}+x}{\mathrm{a}-x}}\]?
What is the value of \[\int\sin^3x\cos^2x\,dx\]?
For \[\int\frac{\sin x}{\sin(x+a)}\,dx\], which substitution gives \[dx=dt\]?
