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
Integrate : sec3 x w. r. t. x.
Evaluate `int_0^(pi)e^2x.sin(pi/4+x)dx`
Integrate the function in x sin x.
Integrate the function in x sin 3x.
Integrate the function in x cos-1 x.
Integrate the function in (sin-1x)2.
Integrate the function in `(xe^x)/(1+x)^2`.
Integrate the function in `sin^(-1) ((2x)/(1+x^2))`.
Evaluate the following : `int cos sqrt(x).dx`
Evaluate the following : `int sin θ.log (cos θ).dθ`
Integrate the following functions w.r.t. x : `e^(2x).sin3x`
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 : `e^x/x [x (logx)^2 + 2 (logx)]`
Choose the correct options from the given alternatives :
`int (1)/(cosx - cos^2x)*dx` =
Choose the correct options from the given alternatives :
`int [sin (log x) + cos (log x)]*dx` =
Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Integrate the following w.r.t.x : sec4x cosec2x
Solve the following differential equation.
(x2 − yx2 ) dy + (y2 + xy2) dx = 0
Evaluate the following.
`int e^x (1/x - 1/x^2)`dx
Choose the correct alternative from the following.
`int (("x"^3 + 3"x"^2 + 3"x" + 1))/("x + 1")^5 "dx"` =
Evaluate: `int ("ae"^("x") + "be"^(-"x"))/("ae"^("x") - "be"^(−"x"))` dx
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
Evaluate: `int "e"^"x"/(4"e"^"2x" -1)` dx
`int 1/sqrt(2x^2 - 5) "d"x`
`int ["cosec"(logx)][1 - cot(logx)] "d"x`
`int 1/x "d"x` = ______ + c
`int logx/(1 + logx)^2 "d"x`
`int [(log x - 1)/(1 + (log x)^2)]^2`dx = ?
`int "dx"/(sin(x - "a")sin(x - "b"))` is equal to ______.
If u and v ore differentiable functions of x. then prove that:
`int uv dx = u intv dx - int [(du)/(d) intv dx]dx`
Hence evaluate `intlog x dx`
Evaluate: `int_0^(pi/4) (dx)/(1 + tanx)`
`int((4e^x - 25)/(2e^x - 5))dx = Ax + B log(2e^x - 5) + c`, then ______.
Evaluate :
`int(4x - 6)/(x^2 - 3x + 5)^(3/2) dx`
Solution of the equation `xdy/dx=y log y` is ______
`int(f'(x))/sqrt(f(x)) dx = 2sqrt(f(x))+c`
Evaluate:
`intcos^-1(sqrt(x))dx`
Evaluate:
`int e^(ax)*cos(bx + c)dx`
Evaluate:
`int e^(logcosx)dx`
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`
If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.
Evaluate:
`int x^2 cos x dx`
The value of `int (x sin^-1)/(sqrt(1 - x^2)) dx` is equal to:
Under the LIATE rule, which type of function has priority \(L\)?
Evaluate \[\int \frac{x\sin^{-1}x}{\sqrt{1-x^2}}\,dx.\]
