Advertisements
Advertisements
प्रश्न
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Advertisements
उत्तर
\[\int \left( \frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} \right)dx\]
\[ \Rightarrow \int \frac{\left( \sin x + \cos x \right)dx}{\sqrt{\sin^2 x + \cos^2 x + 2 \sin x \cos x}}\]
\[ \Rightarrow \int \frac{\left( \sin x + \cos x \right)dx}{\sqrt{\left( \sin x + \cos x \right)^2}}\]
\[ \Rightarrow \int dx\]
\[ \Rightarrow x + C\]
APPEARS IN
संबंधित प्रश्न
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
`x^2/(2+ 3x^3)^3`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Evaluate `int 1/(3+ 2 sinx + cosx) dx`
Write a value of
Write a value of
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`
Integrate the following functions w.r.t. x : sin4x.cos3x
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 : `(4e^x - 25)/(2e^x - 5)`
Integrate the following functions w.r.t. x : tan5x
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Evaluate `int 1/("x" ("x" - 1))` dx
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
Evaluate `int "x - 1"/sqrt("x + 4")` dx
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
Evaluate: `int log ("x"^2 + "x")` dx
`int sqrt(x^2 + 2x + 5)` dx = ______________
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
`int 1/(sinx.cos^2x)dx` = ______.
`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate the following.
`intx sqrt(1 +x^2) dx`
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate `int1/(x(x-1))dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
