Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : `(2x + 1)sqrt(x + 2)`
Advertisements
उत्तर
Let I = `ff(2x + 1)sqrt(x + 2).dx`
Put x + 2 = t
∴ dx = dt
Also, x = t – 2
∴ 2x + 1 = 2(t – 2) + 1 = 2t – 3
∴ I = `int (2t - 3)sqrt(t) dt`
= `int (2t^(3/2) - 3t^(1/2))dt`
= `2int t^(3/2)dt - 3 intt^(1/2)dt`
= `2.(t^5/2)/((5/2)) - 3 . (t^(3/2))/((3/2)) + c`
= `(4)/(5)(x + 2)^(5/2) - 2(x + 2)^(3/2) + c`.
APPEARS IN
संबंधित प्रश्न
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Evaluate :
`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
`e^(2x+3)`
Evaluate: `int 1/(x(x-1)) dx`
Write a value of
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]
Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Evaluate the following:
`int sinx/(sin 3x) dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
Evaluate the following integrals : `int sqrt((9 - x)/x).dx`
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Choose the correct alternative from the following.
The value of `int "dx"/sqrt"1 - x"` is
State whether the following statement is True or False.
If `int x "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.
Evaluate `int 1/((2"x" + 3))` dx
`int x^2/sqrt(1 - x^6)` dx = ________________
`int (log x)/(log ex)^2` dx = _________
`int (7x + 9)^13 "d"x` ______ + c
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
`int sin^-1 x`dx = ?
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
`int(5x + 2)/(3x - 4) dx` = ______
`int ("d"x)/(x(x^4 + 1))` = ______.
`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 the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
