Advertisements
Advertisements
प्रश्न
Write a value of
Advertisements
उत्तर
Let I = ∫ x2 sin x3 dx
⇒ 3x2 dx = dt
\[\Rightarrow x^2 \text{ dx }= \frac{dt}{3}\]
\[ \therefore I = \frac{1}{3}\int \text{ sin t dt}\]
\[ = \frac{1}{3}\left[ - \cos\text{ t }\right] + C\]
\[ = - \frac{1}{3}\cos \text{ x}^3 + C \left( \because t = x^3 \right)\]
APPEARS IN
संबंधित प्रश्न
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Write a value of
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
Integrate the following w.r.t. x:
`2x^3 - 5x + 3/x + 4/x^5`
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Evaluate the following integrals: `int sin 4x cos 3x dx`
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int (cos2x)/(sin^2x) "d"x`
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
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 ______.
`int 1/(sinx.cos^2x)dx` = ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
Evaluate `int (1)/(x(x - 1))dx`
If f'(x) = 4x3- 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate `int 1/(x(x-1))dx`
