Advertisements
Advertisements
Question
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
Advertisements
Solution
Let I = `int sqrt(x)*sec(x^(3/2))*tan(x^(3/2))"d"x`
Put `x^(3/2)` = t
∴ `3/2x^(1/2) "d"x` = dt
∴ `sqrt(x) "d"x = 2/3 "dt"`
∴ I = `2/3 int sec "t"*tan"t"* "dt"`
= `2/3 sec "t" + "c"`
∴ I = `2/3 sec(x^(3/2)) + "c"`
APPEARS IN
RELATED QUESTIONS
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Find `intsqrtx/sqrt(a^3-x^3)dx`
Integrate the functions:
`x/(9 - 4x^2)`
Write a value of
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Integrate the following functions w.r.t. x : tan5x
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Evaluate the following:
`int sinx/(sin 3x) dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: ∫ |x| dx if x < 0
`int x^2/sqrt(1 - x^6)` dx = ________________
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int logx/x "d"x`
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int 1/(xsin^2(logx)) "d"x`
`int(log(logx))/x "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int sec^6 x tan x "d"x` = ______.
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
Evaluate `int 1/("x"("x" - 1)) "dx"`
Evaluate the following.
`int 1/(x^2 + 4x - 5) dx`
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int1/(x(x-1))dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
