Advertisements
Advertisements
Question
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
Options
f(x) − log x + c
f(x) + log x + c
log x − f(x) + c
`1/5x^5` f(x) + c
Solution
log x − f(x) + c
RELATED QUESTIONS
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Find : `int(x+3)sqrt(3-4x-x^2dx)`
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`
Integrate the functions:
sec2(7 – 4x)
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Integrate the functions:
`1/(1 - tan x)`
`int (dx)/(sin^2 x cos^2 x)` equals:
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Evaluate the following integrals : `int sin 4x cos 3x dx`
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t. x : `(2x + 1)sqrt(x + 2)`
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t. x : `(1)/(sinx.cosx + 2cos^2x)`
Integrate the following functions w.r.t.x:
cos8xcotx
Integrate the following functions w.r.t. x : sin5x.cos8x
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Evaluate the following : `int (logx)2.dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
`int logx/(log ex)^2*dx` = ______.
Evaluate `int 1/("x" ("x" - 1))` dx
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^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 1/((2"x" + 3))` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int cos sqrtx` dx = _____________
`int (sin4x)/(cos 2x) "d"x`
`int logx/x "d"x`
Choose the correct alternative:
`int(1 - x)^(-2) dx` = ______.
`int (7x + 9)^13 "d"x` ______ + c
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
`int sin^-1 x`dx = ?
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
`int (cos x)/(1 - sin x) "dx" =` ______.
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.
Evaluate `int 1/("x"("x" - 1)) "dx"`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
Prove that:
`int 1/sqrt(x^2 - a^2) dx = log |x + sqrt(x^2 - a^2)| + c`.
`int x^3 e^(x^2) dx`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
Evaluate `int (1)/(x(x - 1))dx`
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
`int "cosec"^4x dx` = ______.
Evaluate:
`int sin^2(x/2)dx`
`int x^2/sqrt(1 - x^6)dx` = ______.
Evaluate the following.
`int1/(x^2+4x-5) dx`
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
Evaluate the following:
`int x^3/(sqrt(1+x^4))dx`
Evaluate `int1/(x(x-1))dx`
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate `int1/(x(x-1))dx`
If f '(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
Evaluate `int 1/(x(x-1)) dx`
