Advertisements
Advertisements
प्रश्न
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Advertisements
उत्तर
`int (sin4x)/(cos2x).dx`
= `int(2sin 2x cos 2x)/(cos2x).dx`
= `2int sin 2x .dx`
= `2(-(cos2x)/2) + c`
= – cos 2x + c.
APPEARS IN
संबंधित प्रश्न
Evaluate :`intxlogxdx`
Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
`sin x/(1+ cos x)`
Integrate the functions:
`1/(1 - tan x)`
Write a value of
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
Evaluate: `int "e"^sqrt"x"` dx
`int x^2/sqrt(1 - x^6)` dx = ________________
`int sqrt(x^2 + 2x + 5)` dx = ______________
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
`int (cos x)/(1 - sin x) "dx" =` ______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
`int 1/(sinx.cos^2x)dx` = ______.
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
Evaluate the following.
`int 1/(x^2 + 4x - 5) dx`
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
If f '(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate `int 1/(x(x-1))dx`
Evaluate `int1/(x(x - 1))dx`
