Advertisements
Advertisements
प्रश्न
Integrate the functions:
`xsqrt(1+ 2x^2)`
Advertisements
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
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
`xsqrt(x + 2)`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
`int (dx)/(sin^2 x cos^2 x)` equals:
Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`
Write a value of
Write a value of
Write a value of
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following functions w.r.t. x : cos7x
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Evaluate the following.
`int 1/(4x^2 - 20x + 17)` dx
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
`int (sin4x)/(cos 2x) "d"x`
`int x/(x + 2) "d"x`
`int cos^7 x "d"x`
`int(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
`int x/sqrt(1 - 2x^4) dx` = ______.
(where c is a constant of integration)
`int cos^3x dx` = ______.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
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 dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
