Advertisements
Advertisements
प्रश्न
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Advertisements
उत्तर
Let I = `int (3"x"^3 - 2sqrt"x")/"x"` dx
`= int ("3x"^3/"x" - "2x"^(1/2)/"x")` dx
`= int (3"x"^2 - 2"x"^(-1/2))` dx
`= 3 int "x"^2 * "dx" - 2 int "x"^(-1/2) * "dx"`
`= 3 ("x"^3/3) - 2("x"^(1/2)/(1/2))` + c
∴ I = x3 - 4`sqrt"x"` + c
APPEARS IN
संबंधित प्रश्न
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`
Write a value of
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Evaluate the following : `int (logx)2.dx`
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
Choose the correct options from the given alternatives :
`int (cos2x - 1)/(cos2x + 1)*dx` =
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
Choose the correct alternative from the following.
The value of `int "dx"/sqrt"1 - x"` is
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
`int x^x (1 + logx) "d"x`
`int (cos2x)/(sin^2x) "d"x`
`int x/(x + 2) "d"x`
`int x^3 e^(x^2) dx`
Evaluate `int (1)/(x(x - 1))dx`
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate `int1/(x(x-1))dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
In \[\int\sin^3x\cos^2x\,dx\], which rewriting prepares the integrand for the substitution \[t=\cos x\]?
For \[\int\frac{\sin x}{\sin(x+a)}\,dx\], which substitution gives \[dx=dt\]?
