Advertisements
Advertisements
प्रश्न
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
Advertisements
उत्तर
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x5 + `underline((-5)/3)` x3 + 5x + c
Explanation:
`"I" = int (5(x^6 + 1))/(x^2 + 1) "dx"`
`"I" = 5 int ((x^2)^3 + (1)^3)/("x"^2 + 1) "dx"`
`"I" = 5int((cancel("x"^2 + 1))("x"^4 - "x"^2 + 1))/(cancel("x"^2 + 1)) "dx" ...[a^3 + b^3 = (a + b)(a^2 - ab + b^2)]`
`"I" = 5 int ("x"^4 - "x"^2 + 1)` dx
`"I" = 5 ("x"^5/5 - "x"^3/3 + "x") + c ...[int "x"^"n" "dx" = "x"^("n" + 1)/("n" + 1)]`
`"I" = "x"^5 - 5/3"x"^3 + 5"x"` + c
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
sec2(7 – 4x)
Evaluate: `int (sec x)/(1 + cosec x) dx`
\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Evaluate the following integrals : `int sqrt((9 - x)/x).dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
Evaluate `int 1/((2"x" + 3))` dx
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
`int 1/(xsin^2(logx)) "d"x`
`int cot^2x "d"x`
`int1/(4 + 3cos^2x)dx` = ______
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
Evaluate `int(1+ x + x^2/(2!)) dx`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate the following.
`intxsqrt(1+x^2)dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
