Advertisements
Advertisements
प्रश्न
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
विकल्प
`2sqrt(cotx) + c`
`-2sqrt(cotx) + c`
`(1)/(2)sqrt(cotx) + c`
`sqrt(cotx) + c`
उत्तर
`-2sqrt(cotx) + c`
APPEARS IN
संबंधित प्रश्न
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`
Find `intsqrtx/sqrt(a^3-x^3)dx`
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Evaluate `int 1/(3+ 2 sinx + cosx) dx`
Write a value of
Write a value of
Write a value of
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
The value of \[\int\frac{1}{x + x \log x} dx\] is
`int "dx"/(9"x"^2 + 1)= ______. `
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals : `int(x - 2)/sqrt(x + 5).dx`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x : `(1)/(sinx.cosx + 2cos^2x)`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
`int logx/(log ex)^2*dx` = ______.
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
Fill in the Blank.
To find the value of `int ((1 + log "x") "dx")/"x"` the proper substitution is ________
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
State whether the following statement is True or False.
If `int x "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.
State whether the following statement is True or False.
If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int (sin4x)/(cos 2x) "d"x`
`int logx/x "d"x`
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int (cos2x)/(sin^2x) "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
`int sin^-1 x`dx = ?
`int1/(4 + 3cos^2x)dx` = ______
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
`int(log(logx) + 1/(logx)^2)dx` = ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
Evaluate the following
`int1/(x^2 +4x-5)dx`
Evaluate `int 1/("x"("x" - 1)) "dx"`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`intx sqrt(1 +x^2) dx`
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate `int 1/(x(x-1)) dx`
