Advertisements
Advertisements
प्रश्न
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
Advertisements
उत्तर
Let I = `int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
`= int 1/sqrt("x"^2 + 2 * 2"x" + 4 - 4 + 29)` dx
`= int 1/(sqrt(("x + 2")^2 + 25)` dx
`= int "dx"/(sqrt(("x + 2")^2 + 5^2)`
`= log |("x + 2") + sqrt(("x + 2")^2 + 5^2)|`+ c
∴ I = `= log |("x + 2") + sqrt("x"^2 + "4x" + 29)|` + c
Notes
The answer in the textbook is incorrect.
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Solve:
dy/dx = cos(x + y)
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Evaluate the following : `int (1)/(cos2x + 3sin^2x).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 :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Evaluate: ∫ |x| dx if x < 0
`int cot^2x "d"x`
`int(1 - x)^(-2) dx` = ______.
`int(5x + 2)/(3x - 4) dx` = ______
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int ("d"x)/(x(x^4 + 1))` = ______.
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
If f'(x) = `x + 1/x`, then f(x) is ______.
`int (logx)^2/x dx` = ______.
Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.
Evaluate `int(1 + x + x^2/(2!))dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate `int 1/(x(x-1))dx`
If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
`int (x + 1)/(x(1 + xe^x)) dx` is equal to
How should a substitution be chosen?
