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:
`(1+ log x)^2/x`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Solve:
dy/dx = cos(x + y)
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Evaluate the following integrals:
`int (cos2x)/sin^2x dx`
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).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^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sinx).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
Evaluate the following.
`int 1/(4x^2 - 20x + 17)` dx
State whether the following statement is True or False.
If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
The value of `intsinx/(sinx - cosx)dx` equals ______.
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
