Advertisements
Advertisements
प्रश्न
Choose the correct options from the given alternatives :
`int (log (3x))/(xlog (9x))*dx` =
पर्याय
log (3x) – log (9x) + c·
log (x) – (log 3) · log (log 9x) + c
log 9 – (log x) · log (log 3x) + c
log (x) + (log 3) · log (log 9x) + c
Advertisements
उत्तर
log (x) – (log 3) · log (log 9x) + c
[ Hint : `int (log3x)/(xlog(x))*dx = int (log((9x)/3))/(xlog(9x))*dx`
= `int (log (9x) - log3)/(xlog(9x))*dx`
= `int[1/x- (log3)/(xlog(9x))]*dx`
= `int 1/x*dx - (log3) int ((1/x))/(log (9x))*dx`
= log (x) – (log 3) · log (log 9x) + c].
APPEARS IN
संबंधित प्रश्न
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
If u and v are two functions of x then prove that
`intuvdx=uintvdx-int[du/dxintvdx]dx`
Hence evaluate, `int xe^xdx`
Integrate the function in x2 log x.
Integrate the function in x cos-1 x.
Integrate the function in tan-1 x.
Integrate the function in (x2 + 1) log x.
Integrate the function in `(xe^x)/(1+x)^2`.
Integrate the function in `((x- 3)e^x)/(x - 1)^3`.
`int e^x sec x (1 + tan x) dx` equals:
Evaluate the following : `int x^2*cos^-1 x*dx`
Integrate the following functions w.r.t. x: `sqrt(x^2 + 2x + 5)`.
Integrate the following functions w.r.t. x : `[x/(x + 1)^2].e^x`
Integrate the following functions w.r.t.x:
`e^(5x).[(5x.logx + 1)/x]`
If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = ______.
Integrate the following w.r.t.x : log (log x)+(log x)–2
Integrate the following w.r.t.x : log (x2 + 1)
Integrate the following w.r.t.x : e2x sin x cos x
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 (1 - "x")^(-2) "dx"` =
Evaluate: Find the primitive of `1/(1 + "e"^"x")`
Evaluate: `int "dx"/("9x"^2 - 25)`
`int (sin(x - "a"))/(cos (x + "b")) "d"x`
`int ["cosec"(logx)][1 - cot(logx)] "d"x`
`int 1/x "d"x` = ______ + c
Evaluate `int 1/(4x^2 - 1) "d"x`
`int 1/sqrt(x^2 - 8x - 20) "d"x`
`int [(log x - 1)/(1 + (log x)^2)]^2`dx = ?
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`
`int "dx"/(sin(x - "a")sin(x - "b"))` is equal to ______.
The value of `int_(- pi/2)^(pi/2) (x^3 + x cos x + tan^5x + 1) dx` is
State whether the following statement is true or false.
If `int (4e^x - 25)/(2e^x - 5)` dx = Ax – 3 log |2ex – 5| + c, where c is the constant of integration, then A = 5.
`int x/((x + 2)(x + 3)) dx` = ______ + `int 3/(x + 3) dx`
Find the general solution of the differential equation: `e^((dy)/(dx)) = x^2`.
`int 1/sqrt(x^2 - a^2)dx` = ______.
If `int (f(x))/(log(sin x))dx` = log[log sin x] + c, then f(x) is equal to ______.
`intsqrt(1+x) dx` = ______
`int(3x^2)/sqrt(1+x^3) dx = sqrt(1+x^3)+c`
`int (sin^-1 sqrt(x) + cos^-1 sqrt(x))dx` = ______.
Evaluate:
`int (sin(x - a))/(sin(x + a))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).
