Advertisements
Advertisements
प्रश्न
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Advertisements
उत्तर
I = `int (1)/(7 + 2x^2).dx`
= `(1)/(2) int (1)/(7/2 + x^2).dx`
= `(1)/(2) int (1)/((sqrt(7/2))^2 + x^2).dx`
= `(1)/(2).(1)/((sqrt(7/2))) tan^-1 |x/sqrt(7/2)| + c`
= `(1)/sqrt(14)tan^-1 |(sqrt(2)x)/sqrt(7)| + c`.
APPEARS IN
संबंधित प्रश्न
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`1/(1 + cot x)`
Solve:
dy/dx = cos(x + y)
Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Write a value of
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
Evaluate the following integrals:
tan2x dx
Evaluate the following integral:
`int(4x + 3)/(2x + 1).dx`
Evaluate the following integrals : `int cos^2x.dx`
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)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 the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
`int (log x)/(log ex)^2` dx = _________
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int(log(logx))/x "d"x`
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
Evaluate `int (1+x+x^2/(2!))dx`
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
Evaluate:
`int sin^3x cos^3x dx`
Evaluate the following.
`intxsqrt(1+x^2)dx`
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
