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
Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`
Evaluate :
`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`
Integrate the functions:
`(log x)^2/x`
Integrate the functions:
`1/(1 - tan x)`
Integrate the functions:
`(1+ log x)^2/x`
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Solve:
dy/dx = cos(x + y)
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
The value of \[\int\frac{1}{x + x \log x} dx\] is
`int "dx"/(9"x"^2 + 1)= ______. `
Evaluate the following integrals:
`int (cos2x)/sin^2x dx`
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following functions w.r.t.x:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
If f'(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
Evaluate the following.
`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int dx/(1 + e^-x)` = ______
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluate `int(1 + x + x^2/(2!) )dx`
Evaluate `int (1+x+x^2/(2!))dx`
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
Evaluate `int(1 + x + x^2/(2!))dx`
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
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.
`int (5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`intxsqrt(1+x^2)dx`
Evaluate `int1/(x(x-1))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).
Evaluate the following.
`int 1/ (x^2 + 4x - 5) 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).
