Advertisements
Advertisements
प्रश्न
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Advertisements
उत्तर
Let `I = int (e^(tan -1 x)/(1 + x^2))` dx
Put tan-1 x = t
`1/(1 + x^2)` dx = dt
Hence, `I = int e^t` dt
= et + C
= `e^(tan^-1) + C`
APPEARS IN
संबंधित प्रश्न
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Evaluate :
`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`
Integrate the functions:
`e^(2x+3)`
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Evaluate the following integrals: `int sin 4x cos 3x dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(x^2)`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: ∫ |x| dx if x < 0
`int cot^2x "d"x`
`int (1 + x)/(x + "e"^(-x)) "d"x`
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int sec^6 x tan x "d"x` = ______.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate `int1/(x(x - 1))dx`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate:
`int sin^2(x/2)dx`
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
Evaluate `int1/(x(x - 1))dx`
