Advertisements
Advertisements
Question
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Advertisements
Solution
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
RELATED QUESTIONS
Evaluate :`intxlogxdx`
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Integrate the functions:
`x^2/(2+ 3x^3)^3`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Write a value of
Write a value of
Write a value of
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Evaluate the following integrals:
`int (cos2x)/sin^2x dx`
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
`int cos sqrtx` dx = _____________
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate the following.
`intxsqrt(1+x^2)dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
After putting \[t=\cos x\], which integral is obtained from \[\int\sin^2x\cos^2x(\sin x)\,dx\]?
