Advertisements
Advertisements
प्रश्न
Evaluate `int "x - 1"/sqrt("x + 4")` dx
Advertisements
उत्तर
Let I = `int "x - 1"/sqrt("x + 4")` dx
= `int (("x + 4") - 5)/sqrt("x + 4")` dx
= `int (sqrt"x + 4" - 5/(sqrt "x + 4"))` dx
`= int [("x + 4")^(1/2) - 5("x + 4")^(- 1/2)]` dx
`= ("x + 4")^(3/2)/(3/2) - 5 ("x + 4")^(1/2)/(1/2)` + c
∴ I = `2/3 ("x + 4")^(3/2) - 10 sqrt("x + 4")` + c
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`cos sqrt(x)/sqrtx`
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Write a value of
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Write a value of
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
`int sqrt(1 + "x"^2) "dx"` =
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
Evaluate `int (5"x" + 1)^(4/9)` dx
Evaluate: `int 1/(sqrt("x") + "x")` dx
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
