Advertisements
Advertisements
Question
`int cos sqrtx` dx = _____________
Options
`2 [sqrtx sin sqrtx + cos sqrtx] + "c"`
`sqrtx sin sqrtx + cos sqrtx + "c"`
`2 [sqrtx cos sqrtx + sin sqrtx] + "c"`
`1/2 [sqrtx sin sqrtx - cos sqrtx] + "c"`
Advertisements
Solution
`2 [sqrtx sin sqrtx + cos sqrtx] + "c"`
APPEARS IN
RELATED QUESTIONS
Integrate the functions:
`e^(2x+3)`
Write a value of
Write a value of
Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
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 : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Evaluate the following : `int (logx)2.dx`
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int x^2/sqrt(1 - x^6)` dx = ________________
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int (log x)/(log ex)^2` dx = _________
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
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"`
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
`int(5x + 2)/(3x - 4) dx` = ______
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
The value of `intsinx/(sinx - cosx)dx` equals ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
Write `int cotx dx`.
Find `int dx/sqrt(sin^3x cos(x - α))`.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate the following
`int1/(x^2 +4x-5)dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate `int (1)/(x(x - 1))dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
After choosing \[u=g(x)\], what is the next step?
In \[\int\sin^3x\cos^2x\,dx\], which rewriting prepares the integrand for the substitution \[t=\cos x\]?
