Advertisements
Advertisements
प्रश्न
Choose the correct options from the given alternatives :
`int cos -(3)/(7)x*sin -(11)/(7)x*dx` =
पर्याय
`log (sin^(-4/7) x) + c`
`(4)/(7)tan^(4/7) x + c`
`-(7)/(4)tan^(-4/7) x + c`
`log (cos^(3/7) x) + c`
Advertisements
उत्तर
`-(7)/(4)tan^(-4/7) x + c`
[ Hint : `int cos^(-3/7)x sin^(-11/7)x*dx`
= `int (sin^(-11/7)x)/(cos^(-11/7)x*cos^2x)*dx`
= `int tan^(-11/7)x sec^2x*dx`
Put tan x = t].
APPEARS IN
संबंधित प्रश्न
Prove that: `int sqrt(a^2 - x^2) * dx = x/2 * sqrt(a^2 - x^2) + a^2/2 * sin^-1(x/a) + c`
Prove that:
`int sqrt(x^2 - a^2)dx = x/2sqrt(x^2 - a^2) - a^2/2log|x + sqrt(x^2 - a^2)| + c`
If `int_(-pi/2)^(pi/2)sin^4x/(sin^4x+cos^4x)dx`, then the value of I is:
(A) 0
(B) π
(C) π/2
(D) π/4
Integrate the function in x log x.
Integrate the function in `(x cos^(-1) x)/sqrt(1-x^2)`.
Find :
`∫(log x)^2 dx`
Evaluate the following:
`int x tan^-1 x . dx`
Evaluate the following : `int x^3.logx.dx`
Evaluate the following : `int (t.sin^-1 t)/sqrt(1 - t^2).dt`
Evaluate the following : `int cos sqrt(x).dx`
Evaluate the following : `int(sin(logx)^2)/x.log.x.dx`
Integrate the following functions w.r.t. x:
sin (log x)
Integrate the following functions w.r.t. x : `sqrt(5x^2 + 3)`
Integrate the following functions w.r.t. x : `sqrt(4^x(4^x + 4))`
Integrate the following functions w.r.t. x : `sqrt(2x^2 + 3x + 4)`
Integrate the following functions w.r.t. x : [2 + cot x – cosec2x]ex
Integrate the following functions w.r.t.x:
`e^(5x).[(5x.logx + 1)/x]`
Choose the correct options from the given alternatives :
`int (1)/(x + x^5)*dx` = f(x) + c, then `int x^4/(x + x^5)*dx` =
Integrate the following w.r.t.x : sec4x cosec2x
Evaluate the following.
`int x^3 e^(x^2)`dx
Evaluate the following.
`int (log "x")/(1 + log "x")^2` dx
Evaluate: Find the primitive of `1/(1 + "e"^"x")`
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
`int (sin(x - "a"))/(cos (x + "b")) "d"x`
`int (cos2x)/(sin^2x cos^2x) "d"x`
Evaluate `int 1/(x log x) "d"x`
`int logx/(1 + logx)^2 "d"x`
The value of `int "e"^(5x) (1/x - 1/(5x^2)) "d"x` is ______.
Evaluate the following:
`int ((cos 5x + cos 4x))/(1 - 2 cos 3x) "d"x`
The value of `int_(- pi/2)^(pi/2) (x^3 + x cos x + tan^5x + 1) dx` is
Evaluate: `int_0^(pi/4) (dx)/(1 + tanx)`
Find the general solution of the differential equation: `e^((dy)/(dx)) = x^2`.
`int(logx)^2dx` equals ______.
`intsqrt(1+x) dx` = ______
`int(3x^2)/sqrt(1+x^3) dx = sqrt(1+x^3)+c`
The integrating factor of `ylogy.dx/dy+x-logy=0` is ______.
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4))dx`
Evaluate `int tan^-1x dx`
Evaluate:
`int1/(x^2 + 25)dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate `int (1 + x + x^2/(2!))dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate \[\int \frac{x\sin^{-1}x}{\sqrt{1-x^2}}\,dx.\]
