Advertisements
Advertisements
प्रश्न
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Advertisements
उत्तर
Let I = `int x^3/sqrt(1 + x^4)` dx
Put 1 + x4 = t
∴ 4x3 . dx = dt
∴ x3 . dx = `1/4` dt
∴ I = `1/4 int dt/sqrtt`
`= 1/4 int t^((-1)/2)`dt
`= 1/4 * t^(1/2)/(1/2)` + c
`= 1/2 sqrtt + c`
∴ I = `1/2 sqrt(1 + x^4)` + c
संबंधित प्रश्न
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`x^2/(2+ 3x^3)^3`
Integrate the functions:
`x/(9 - 4x^2)`
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Evaluate the following integral:
`int(4x + 3)/(2x + 1).dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Choose the correct options from the given alternatives :
`int (cos2x - 1)/(cos2x + 1)*dx` =
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
Evaluate the following.
`int 1/(x(x^6 + 1))` 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.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
Evaluate: `int "e"^sqrt"x"` dx
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int x^x (1 + logx) "d"x`
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
`int(log(logx) + 1/(logx)^2)dx` = ______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) 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`
Which substitution is appropriate for \[\sqrt{\frac{x}{a-x}}\], \[\sqrt{\frac{a-x}{x}}\], \[\sqrt{x(a-x)}\], or \[\frac{1}{\sqrt{x(a-x)}}\]?
After putting \[t=\cos x\], which integral is obtained from \[\int\sin^2x\cos^2x(\sin x)\,dx\]?
For \[\int\frac{\sin x}{\sin(x+a)}\,dx\], which substitution gives \[dx=dt\]?
