Advertisements
Advertisements
प्रश्न
Choose the correct options from the given alternatives :
`int cos -(3)/(7)x*sin -(11)/(7)x*dx` =
विकल्प
`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
उत्तर
`-(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
संबंधित प्रश्न
Prove that: `int sqrt(a^2 - x^2) * dx = x/2 * sqrt(a^2 - x^2) + a^2/2 * sin^-1(x/a) + c`
Integrate : sec3 x w. r. t. x.
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 tan-1 x.
Integrate the function in `(xe^x)/(1+x)^2`.
Integrate the function in `e^x (1/x - 1/x^2)`.
Evaluate the following:
`int x tan^-1 x . dx`
Evaluate the following : `int x.sin^2x.dx`
Evaluate the following : `int cos sqrt(x).dx`
Evaluate the following : `int(sin(logx)^2)/x.log.x.dx`
Integrate the following functions w.r.t. x : `sqrt(5x^2 + 3)`
Integrate the following functions w.r.t. x : `(x + 1) sqrt(2x^2 + 3)`
Integrate the following functions w.r.t. x : `xsqrt(5 - 4x - x^2)`
Integrate the following functions w.r.t.x:
`e^(5x).[(5x.logx + 1)/x]`
Choose the correct options from the given alternatives :
`int tan(sin^-1 x)*dx` =
Choose the correct options from the given alternatives :
`int (x- sinx)/(1 - cosx)*dx` =
Integrate the following with respect to the respective variable : cos 3x cos 2x cos x
Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Integrate the following w.r.t.x : log (log x)+(log x)–2
Evaluate the following.
`int x^2 *e^(3x)`dx
Evaluate the following.
`int [1/(log "x") - 1/(log "x")^2]` dx
`int ("x" + 1/"x")^3 "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"/(3 - 2"x" - "x"^2)`
Evaluate: `int "dx"/("x"[(log "x")^2 + 4 log "x" - 1])`
Evaluate: `int "dx"/(5 - 16"x"^2)`
`int 1/sqrt(2x^2 - 5) "d"x`
`int sin4x cos3x "d"x`
`int ("e"^xlog(sin"e"^x))/(tan"e"^x) "d"x`
`int"e"^(4x - 3) "d"x` = ______ + c
`int [(log x - 1)/(1 + (log x)^2)]^2`dx = ?
Evaluate the following:
`int ((cos 5x + cos 4x))/(1 - 2 cos 3x) "d"x`
`int 1/sqrt(x^2 - 9) dx` = ______.
Find: `int e^x.sin2xdx`
`int(logx)^2dx` equals ______.
`int_0^1 x tan^-1 x dx` = ______.
If `int (f(x))/(log(sin x))dx` = log[log sin x] + c, then f(x) is equal to ______.
`intsqrt(1+x) dx` = ______
Evaluate:
`int(1+logx)/(x(3+logx)(2+3logx)) dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4))dx`
Solve the following
`int_0^1 e^(x^2) x^3 dx`
Evaluate:
`int((1 + sinx)/(1 + cosx))e^x dx`
Evaluate:
`int (logx)^2 dx`
Evaluate the following.
`intx^3 e^(x^2) dx`
Evaluate the following:
`intx^3e^(x^2)dx`
If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.
`∫ sin^(−1)` xdx is equal to ______.
