Advertisements
Advertisements
प्रश्न
Integrate the functions:
`cos sqrt(x)/sqrtx`
Advertisements
उत्तर
Let I = `int (cos sqrtx)/sqrtx` dx
Put `sqrt x = t`
`1/(2 sqrt x)` dx = dt or `1/sqrt x` dx = 2 dt
Hence, `I = 2 int cos t dt`
`= 2 sin t + C = 2 sin sqrt x + C`
APPEARS IN
संबंधित प्रश्न
Evaluate :`intxlogxdx`
Find `intsqrtx/sqrt(a^3-x^3)dx`
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
Write a value of
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
Integrate the following w.r.t. x : x3 + x2 – x + 1
Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int 1/("x" log "x")`dx
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
Evaluate `int (5"x" + 1)^(4/9)` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int 1/(cos x - sin x)` dx = _______________
`int cos sqrtx` dx = _____________
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
Write `int cotx dx`.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Evaluate `int1/(x(x - 1))dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate:
`int sin^3x cos^3x dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
