Advertisements
Advertisements
प्रश्न
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Advertisements
उत्तर
Let `I = int (4x + 2) sqrt(x^2 + x + 1)` dx
or `I = 2 int (2x + 1) sqrt ((x^2 + x + 1))` dx
Taking x2 + x + 1 = t
2x + 1 = dt
Hence, `I = 2 int sqrt t dt`
`= 2 int t^(1/2) dt = 2. 2/3 t^(3/2) + C`
`= 4/3 (x^2 + x + 1)^(3/2) + C`
APPEARS IN
संबंधित प्रश्न
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`xsqrt(x + 2)`
Integrate the functions:
`sin x/(1+ cos x)`
Write a value of
Write a value of
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Write a value of\[\int \log_e x\ dx\].
Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Evaluate the following integrals : `int cos^2x.dx`
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
Evaluate `int (1+x+x^2/(2!)) dx`
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`int 1/ (x^2 + 4x - 5) 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).
