Advertisements
Advertisements
Question
Choose the correct options from the given alternatives :
`int cos -(3)/(7)x*sin -(11)/(7)x*dx` =
Options
`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
Solution
`-(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
RELATED QUESTIONS
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`
Integrate the function in x2 log x.
Integrate the function in tan-1 x.
Integrate the function in `e^x (1 + sin x)/(1+cos x)`.
Integrate the function in `((x- 3)e^x)/(x - 1)^3`.
Evaluate the following : `int e^(2x).cos 3x.dx`
Evaluate the following: `int x.sin^-1 x.dx`
Evaluate the following : `int cos sqrt(x).dx`
Integrate the following functions w.r.t.x:
`e^-x cos2x`
Integrate the following functions w.r.t. x : `sec^2x.sqrt(tan^2x + tan x - 7)`
Integrate the following functions w.r.t. x : `sqrt(2x^2 + 3x + 4)`
Integrate the following functions w.r.t.x:
`e^(5x).[(5x.logx + 1)/x]`
Integrate the following with respect to the respective variable : cos 3x cos 2x cos x
Integrate the following w.r.t.x : log (x2 + 1)
Solve the following differential equation.
(x2 − yx2 ) dy + (y2 + xy2) dx = 0
Evaluate the following.
`int "x"^2 *"e"^"3x"`dx
Evaluate the following.
`int "e"^"x" "x - 1"/("x + 1")^3` dx
Evaluate the following.
`int [1/(log "x") - 1/(log "x")^2]` dx
Evaluate: `int "dx"/(5 - 16"x"^2)`
`int (sinx)/(1 + sin x) "d"x`
`int ["cosec"(logx)][1 - cot(logx)] "d"x`
`int 1/(x^2 - "a"^2) "d"x` = ______ + c
`int"e"^(4x - 3) "d"x` = ______ + c
`int (x^2 + x - 6)/((x - 2)(x - 1)) "d"x` = x + ______ + c
Evaluate `int 1/(x log x) "d"x`
`int "e"^x x/(x + 1)^2 "d"x`
∫ log x · (log x + 2) dx = ?
`int cot "x".log [log (sin "x")] "dx"` = ____________.
`int "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.
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 ______.
If `int(2e^(5x) + e^(4x) - 4e^(3x) + 4e^(2x) + 2e^x)/((e^(2x) + 4)(e^(2x) - 1)^2)dx = tan^-1(e^x/a) - 1/(b(e^(2x) - 1)) + C`, where C is constant of integration, then value of a + b is equal to ______.
The integral `int x cos^-1 ((1 - x^2)/(1 + x^2))dx (x > 0)` is equal to ______.
`int e^x [(2 + sin 2x)/(1 + cos 2x)]dx` = ______.
Find `int e^x ((1 - sinx)/(1 - cosx))dx`.
`int1/sqrt(x^2 - a^2) dx` = ______
Evaluate:
`inte^x sinx dx`
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 `int tan^-1x 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.
`intx^2e^(4x)dx`
Evaluate the following.
`intx^3/(sqrt(1 + x^4))dx`
