Advertisements
Advertisements
प्रश्न
Evaluate: `int (2y^2)/(y^2 + 4)dx`
उत्तर
`I = int (2y^2)/(y^2 + 4) dy`
`= int(2y^2 + 8 - 8)/(y^2 + 4) dy`
`= 2int (y^2 + 4)/(y^2 + 4) dy - 8 int dy/(y^2 + 2^2)`
`= 2y - 4tan^(-1) (y/2) + c`
APPEARS IN
संबंधित प्रश्न
Find : `int(x+3)sqrt(3-4x-x^2dx)`
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
Integrate the following w.r.t. x:
`2x^3 - 5x + 3/x + 4/x^5`
Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(x^2)`
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 : `(x^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t.x:
cos8xcotx
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` 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 "x" * "e"^"2x"` dx
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int (sin4x)/(cos 2x) "d"x`
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int (cos x)/(1 - sin x) "dx" =` ______.
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int sec^6 x tan x "d"x` = ______.
`int (logx)^2/x dx` = ______.
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate the following.
`int1/(x^2+4x-5)dx`