Advertisements
Advertisements
Question
Choose the correct options from the given alternatives :
`int sin (log x)*dx` =
Options
`x/(2)[sin (log x) - cos (log x)] + c`
`x/(2)[sin (log x) + cos (log x)] + c`
`x/(2)[cos (log x) - sin (log x)] + c`
`x/(4)[cos (log x) - sin (log x)] + c`
Advertisements
Solution
`x/(2)[sin (log x) - cos (log x)] + c`
APPEARS IN
RELATED QUESTIONS
Prove that: `int sqrt(a^2 - x^2) * dx = x/2 * sqrt(a^2 - x^2) + a^2/2 * sin^-1(x/a) + c`
Integrate : sec3 x w. r. t. x.
Integrate the function in `(x cos^(-1) x)/sqrt(1-x^2)`.
Integrate the function in ex (sinx + cosx).
Integrate the function in `e^x (1 + sin x)/(1+cos x)`.
Evaluate the following : `int x^2*cos^-1 x*dx`
Evaluate the following : `int sin θ.log (cos θ).dθ`
Evaluate the following: `int logx/x.dx`
Evaluate the following : `int cos(root(3)(x)).dx`
Integrate the following functions w.r.t. x : `e^(2x).sin3x`
Integrate the following functions w.r.t. x : `sqrt(5x^2 + 3)`
Integrate the following functions w.r.t. x : `xsqrt(5 - 4x - x^2)`
Integrate the following functions w.r.t. x : `e^x .(1/x - 1/x^2)`
Integrate the following functions w.r.t. x : `[x/(x + 1)^2].e^x`
Choose the correct options from the given alternatives :
`int (sin^m x)/(cos^(m+2)x)*dx` =
If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = ______.
Integrate the following with respect to the respective variable : cos 3x cos 2x cos x
Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Integrate the following w.r.t.x : `log (1 + cosx) - xtan(x/2)`
Integrate the following w.r.t.x : log (log x)+(log x)–2
Evaluate the following.
`int x^2 *e^(3x)`dx
Evaluate the following.
`int "e"^"x" "x - 1"/("x + 1")^3` dx
Choose the correct alternative from the following.
`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx"` =
Evaluate: `int "e"^"x"/(4"e"^"2x" -1)` dx
`int (cos2x)/(sin^2x cos^2x) "d"x`
`int sin4x cos3x "d"x`
`int 1/x "d"x` = ______ + c
`int (x^2 + x - 6)/((x - 2)(x - 1)) "d"x` = x + ______ + c
Evaluate `int 1/(x(x - 1)) "d"x`
`int "e"^x x/(x + 1)^2 "d"x`
`int 1/sqrt(x^2 - 8x - 20) "d"x`
Evaluate the following:
`int_0^pi x log sin x "d"x`
The value of `int_(- pi/2)^(pi/2) (x^3 + x cos x + tan^5x + 1) dx` is
Find `int (sin^-1x)/(1 - x^2)^(3//2) dx`.
Find `int e^x ((1 - sinx)/(1 - cosx))dx`.
`intsqrt(1+x) dx` = ______
`int logx dx = x(1+logx)+c`
`int(f'(x))/sqrt(f(x)) dx = 2sqrt(f(x))+c`
Evaluate:
`int (logx)^2 dx`
The value of `int e^x((1 + sinx)/(1 + cosx))dx` is ______.
Evaluate:
`int1/(x^2 + 25)dx`
Evaluate the following.
`intx^3 e^(x^2) dx`
Evaluate the following.
`intx^3e^(x^2) dx`
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`intx^2e^(4x)dx`
Evaluate the following.
`intx^3/(sqrt(1 + x^4))dx`
