Advertisements
Advertisements
Question
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Advertisements
Solution
Let I = `int(1)/(4x + 5x^-11).dx`
= `int x_11/(x^11(4x + 5x^-11)).dx`
= `int x^11/(4x^12 + 5).dx`
= `(1)/(48) int(48x^11)/(4x^12 + 5).dx`
= `(1)/(48) int(d/dx(4x^12 + 5))/(4x^12 + 5).dx`
= `(1)/(48)log|4x^12 + 5| + c ...[∵ int (f'(x))/f(x) dx = log|f(x)| + c]`
APPEARS IN
RELATED QUESTIONS
Find: `int(x+3)sqrt(3-4x-x^2dx)`
Integrate the functions:
`(2x)/(1 + x^2)`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
`int (dx)/(sin^2 x cos^2 x)` equals:
Write a value of
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
The value of \[\int\frac{1}{x + x \log x} dx\] is
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`
Evaluate the following integrals: `int sin 4x cos 3x dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Integrate the following functions w.r.t. x : sin4x.cos3x
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following functions w.r.t. x : `(2x + 1)sqrt(x + 2)`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
`int(5x + 2)/(3x - 4) dx` = ______
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int1/(4 + 3cos^2x)dx` = ______
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
Evaluate:
`int sin^2(x/2)dx`
Evaluate the following:
`int x^3/(sqrt(1+x^4))dx`
Evaluate `int1/(x(x-1))dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate `int1/(x(x-1))dx`
If f '(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
