Advertisements
Advertisements
Question
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Advertisements
Solution
\[\text{ Let I} = \int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2}dx\]
\[\text{ Let tan}^{- 1} x = t\]
\[ \Rightarrow \frac{1}{1 + x^2}dx = dt\]
\[ \therefore I = \int t^3 . dt\]
\[ = \frac{t^4}{4} + C\]
\[ = \frac{\left( \tan^{- 1} x \right)^4}{4} + C \left( \because t = \tan^{- 1} x \right)\]
APPEARS IN
RELATED QUESTIONS
Find: `int(x+3)sqrt(3-4x-x^2dx)`
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Evaluate: `int 1/(x(x-1)) dx`
Solve:
dy/dx = cos(x + y)
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following functions w.r.t.x:
cos8xcotx
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following : `int (logx)2.dx`
`int logx/(log ex)^2*dx` = ______.
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
Evaluate: ∫ |x| dx if x < 0
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
If `int(cosx - sinx)/sqrt(8 - sin2x)dx = asin^-1((sinx + cosx)/b) + c`. where c is a constant of integration, then the ordered pair (a, b) is equal to ______.
Write `int cotx dx`.
`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate the following.
`intx sqrt(1 +x^2) dx`
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate `int(1+x+x^2/(2!))dx`
