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
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
Evaluate `int 1/(3+ 2 sinx + cosx) dx`
Write a value of
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
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 : `cosx/sin(x - a)`
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
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 (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
`int (sin4x)/(cos 2x) "d"x`
`int logx/x "d"x`
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
`int 1/(a^2 - x^2) dx = 1/(2a) xx` ______.
Find `int dx/sqrt(sin^3x cos(x - α))`.
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
Evaluate `int1/(x(x - 1))dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate `int1/(x(x-1))dx`
Evaluate `int1/(x(x - 1))dx`
Evaluate `int 1/(x(x-1)) dx`
`int (x + 1)/(x(1 + xe^x)) dx` is equal to
For \[t=\cos x\], what is \[dt\]?
