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
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Evaluate: `int 1/(x(x-1)) dx`
Write a value of
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Integrate the following function w.r.t. x:
x9.sec2(x10)
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 : `(20 + 12e^x)/(3e^x + 4)`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Evaluate `int 1/(x (x - 1))` dx
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
State whether the following statement is True or False.
If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
Evaluate the following.
`int 1/(x^2+4x-5) dx`
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate the following:
`int x^3/(sqrt(1+x^4))dx`
