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:
`(log x)^2/x`
Integrate the functions:
sec2(7 – 4x)
Evaluate: `int 1/(x(x-1)) dx`
Solve:
dy/dx = cos(x + y)
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : `(3e^(2x) + 5)/(4e^(2x) - 5)`
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate: `int "e"^sqrt"x"` dx
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int x/(x + 2) "d"x`
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
Evaluate `int (1)/(x(x - 1))dx`
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
Evaluate:
`int sin^2(x/2)dx`
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Evaluate `int1/(x(x-1))dx`
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
