Advertisements
Advertisements
प्रश्न
Integrate the functions:
`xsqrt(1+ 2x^2)`
उत्तर
Let `I = int x sqrt(1 + 2x^2)` dx
Taking 1 + 2x2 = t
4x dx = dt
or x dx `= 1/4` dt
Hence, `I = int 1/4 t^(1/2) dt = 1/4 int t^(1/2)` dt
`= 1/4 . 2/3 t^(3/2) + C`
`= 1/6 (1 + 2x^2)^(3/2) + C`
APPEARS IN
संबंधित प्रश्न
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
sec2(7 – 4x)
Write a value of
Write a value of
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Integrate the following functions w.r.t.x:
cos8xcotx
Integrate the following functions w.r.t. x : cos7x
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Evaluate the following : `int (logx)2.dx`
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int cos^7 x "d"x`
`int(5x + 2)/(3x - 4) dx` = ______
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
`int secx/(secx - tanx)dx` equals ______.
Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.
`int x^3 e^(x^2) dx`
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate `int1/(x(x - 1))dx`
If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
