Advertisements
Advertisements
प्रश्न
Integrate the following w.r.t.x : `sqrt(tanx)/(sinx*cosx)`
Advertisements
उत्तर
Let I = `int sqrt(tanx)/(sinx*cosx)*dx`
Dividing numerator and denominator by cos2x, we get
I = `int (((sqrt(tanx))/(cos^2)))/(((sinx)/(cosx)))*dx`
= `int (sqrt(tanx)*sec^2x)/tanx*dx`
= `int (sec^2x)/sqrt(tanx)*dx`
Put tan x = t
∴ sec2x·dx = dt
∴ I = `int (1)/sqrt(t)*dt`
= `int t^(-1/2)*dt`
= `t^(1/2)/(1/2) + c`
= `2sqrt(t) + c`
= `2sqrt(tanx) + c`.
APPEARS IN
संबंधित प्रश्न
Evaluate:
`int x^2/(x^4+x^2-2)dx`
Integrate the rational function:
`1/(x^2 - 9)`
Integrate the rational function:
`(1 - x^2)/(x(1-2x))`
Integrate the rational function:
`1/(x(x^4 - 1))`
Integrate the rational function:
`1/(e^x -1)`[Hint: Put ex = t]
Evaluate : `∫(x+1)/((x+2)(x+3))dx`
Integrate the following w.r.t. x : `x^2/((x^2 + 1)(x^2 - 2)(x^2 + 3))`
Integrate the following w.r.t. x : `(2x)/(4 - 3x - x^2)`
Integrate the following w.r.t. x : `(x^2 + x - 1)/(x^2 + x - 6)`
Integrate the following w.r.t. x : `(1)/(x(x^5 + 1)`
Integrate the following w.r.t. x : `(3x - 2)/((x + 1)^2(x + 3)`
Integrate the following w.r.t. x : `(1)/(x(1 + 4x^3 + 3x^6)`
Integrate the following w.r.t. x: `(1)/(sinx + sin2x)`
Integrate the following w.r.t. x : `(5*e^x)/((e^x + 1)(e^(2x) + 9)`
Choose the correct options from the given alternatives :
If `int tan^3x*sec^3x*dx = (1/m)sec^mx - (1/n)sec^n x + c, "then" (m, n)` =
Integrate the following with respect to the respective variable : `(6x + 5)^(3/2)`
Integrate the following w.r.t.x : `(1)/((1 - cos4x)(3 - cot2x)`
Integrate the following w.r.t.x : `(1)/(2cosx + 3sinx)`
Integrate the following w.r.t.x : `sec^2x sqrt(7 + 2 tan x - tan^2 x)`
Evaluate: `int 1/("x"("x"^5 + 1))` dx
Evaluate: `int (5"x"^2 + 20"x" + 6)/("x"^3 + 2"x"^2 + "x")` dx
Evaluate: `int ("3x" - 1)/("2x"^2 - "x" - 1)` dx
Evaluate: `int (2"x"^3 - 3"x"^2 - 9"x" + 1)/("2x"^2 - "x" - 10)` dx
Evaluate: `int (1 + log "x")/("x"(3 + log "x")(2 + 3 log "x"))` dx
`int (2x - 7)/sqrt(4x- 1) dx`
`int x^7/(1 + x^4)^2 "d"x`
If f'(x) = `x - 3/x^3`, f(1) = `11/2` find f(x)
`int sqrt((9 + x)/(9 - x)) "d"x`
`int (sinx)/(sin3x) "d"x`
`int x^3tan^(-1)x "d"x`
`int x^2/((x^2 + 1)(x^2 - 2)(x^2 + 3)) "d"x`
`int xcos^3x "d"x`
`int (sin2x)/(3sin^4x - 4sin^2x + 1) "d"x`
Evaluate the following:
`int "e"^(-3x) cos^3x "d"x`
Evaluate:
`int 2/((1 - x)(1 + x^2))dx`
Evaluate:
`int(2x^3 - 1)/(x^4 + x)dx`
When is a rational function called improper?
Integration by partial fractions is a method used to integrate which functions?
What should be checked before beginning partial-fraction decomposition?
What is the result of dividing \[x^{2}+1\] by \[x^{2}-5x+6\]?
For \[\frac{5x-5}{(x-2)(x-3)}=\frac{\mathrm{A}}{x-2}+\frac{\mathrm{B}}{x-3}\], which equation results after clearing denominators?
What must be included for a repeated linear factor?
What numerator is used for an irreducible quadratic factor?
