Advertisements
Advertisements
Question
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Advertisements
Solution
Let `I = int (x^3 sin (tan^-1 x^4))/(1 + x^8)` dx
Put tan-1 x4 = t
or `1/(1 + x^8) * 4x^3 dx = dt`
`1/(1 + x^8). x^3 = 1/4 dt`
Hence, `I = 1/4 int sin t dt`
`= - 1/4 cos t + C`
`= - 1/4 cos (tan^-1 x^4) + C`
APPEARS IN
RELATED QUESTIONS
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
`e^(2x+3)`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Integrate the functions:
`1/(1 + cot x)`
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Integrate the following functions w.r.t. x : tan5x
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Evaluate the following.
`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
`int sqrt(1 + "x"^2) "dx"` =
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
State whether the following statement is True or False.
If `int x "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int x/(x + 2) "d"x`
`int dx/(1 + e^-x)` = ______
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
If f'(x) = `x + 1/x`, then f(x) is ______.
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
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)
`int x^3 e^(x^2) dx`
Evaluate the following:
`int x^3/(sqrt(1+x^4))dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
