Advertisements
Advertisements
Question
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` =
Options
log x – f(x) + c
f(x) + log x + c
f(x) – log x + c
`(1)/(5) x^5f(x) + c`
Advertisements
Solution
log x – f(x) + c
[Hint: `int x^4/(x + x^5)*dx = int((x^4 + 1) - 1)/(x(x^4 + 1))*dx`
= `int (1/x - 1/(x + x^5))*dx`
= log x – f(x) + c].
APPEARS IN
RELATED QUESTIONS
Integrate the function in `x^2e^x`.
Integrate the function in x2 log x.
Integrate the function in x sin−1 x.
Integrate the function in x tan-1 x.
Integrate the function in `(x cos^(-1) x)/sqrt(1-x^2)`.
Integrate the function in x (log x)2.
Integrate the function in `e^x (1/x - 1/x^2)`.
Integrate the function in e2x sin x.
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`
Evaluate the following : `int x^2tan^-1x.dx`
Evaluate the following : `int x^3.tan^-1x.dx`
Evaluate the following : `int x.sin^2x.dx`
Evaluate the following : `int log(logx)/x.dx`
Integrate the following functions w.r.t.x:
`e^-x cos2x`
Integrate the following functions w.r.t. x:
sin (log x)
Integrate the following functions w.r.t. x : `[x/(x + 1)^2].e^x`
Integrate the following functions w.r.t. x : cosec (log x)[1 – cot (log x)]
Choose the correct options from the given alternatives :
`int (1)/(cosx - cos^2x)*dx` =
Integrate the following with respect to the respective variable : cos 3x cos 2x cos x
Integrate the following w.r.t.x : cot–1 (1 – x + x2)
Integrate the following w.r.t.x : log (log x)+(log x)–2
Integrate the following w.r.t.x : log (x2 + 1)
`int (sin(x - "a"))/(cos (x + "b")) "d"x`
`int sin4x cos3x "d"x`
`int 1/(x^2 - "a"^2) "d"x` = ______ + c
`int (x^2 + x - 6)/((x - 2)(x - 1)) "d"x` = x + ______ + c
Evaluate `int 1/(x(x - 1)) "d"x`
Evaluate `int (2x + 1)/((x + 1)(x - 2)) "d"x`
`int "e"^x x/(x + 1)^2 "d"x`
`int logx/(1 + logx)^2 "d"x`
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`
`int x/((x + 2)(x + 3)) dx` = ______ + `int 3/(x + 3) dx`
`int e^x [(2 + sin 2x)/(1 + cos 2x)]dx` = ______.
`int_0^1 x tan^-1 x dx` = ______.
`int((4e^x - 25)/(2e^x - 5))dx = Ax + B log(2e^x - 5) + c`, then ______.
Find: `int e^(x^2) (x^5 + 2x^3)dx`.
`int(1-x)^-2 dx` = ______
Solution of the equation `xdy/dx=y log y` is ______
Evaluate:
`int(1+logx)/(x(3+logx)(2+3logx)) dx`
`int1/(x+sqrt(x)) dx` = ______
Evaluate `int(3x-2)/((x+1)^2(x+3)) dx`
`int(xe^x)/((1+x)^2) dx` = ______
Evaluate the following:
`intx^3e^(x^2)dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
The value of `inta^x.e^x dx` equals
