-sin x-cos x-1-sin 2xdx-

The correct option is C |x|+c ∫sin x+cos x√(1+sin 2x)dx ∫sin x+cos x√(1+2sin x.cos x)dx =∫sin x+cos x√(sin ^2x+cos ^2+2sin x.cos x)dx ...

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Magnetic Field Due to Straight Current Carrying Conductor

∫sin x+cos x/...

Question

$\int \frac{sin x + cos x}{\sqrt{1 + sin 2 x}} d x =$

x + c

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- x + c

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sin x - c o s x + c

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| x | + c

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Solution

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Similar questions

\int \frac{sin x + cos x}{\sqrt{1 + sin 2 x}} d x

sin x + cos x \geq 0

I = \int \frac{{sin}^{2} x + sin x}{1 + sin x + cos x} d x

J = \int \frac{{cos}^{2} x + cos x}{1 + sin x + cos x} d x

c

\begin{matrix} Function & Integral \begin{matrix} (a) I \end{matrix} & (p) \frac{1}{2} (x - sin x - cos x) + c \begin{matrix} (b) J \end{matrix} & (q) \frac{1}{2} (x + sin x + cos x) + c \begin{matrix} (c) I + J \end{matrix} & (r) x + c \begin{matrix} (d) I - J \end{matrix} & (s) c - cos x - sin x \begin{matrix} \end{matrix} & (t) c + cos x + sin x \begin{matrix} \end{matrix} & (u) - \frac{1}{2} (x + sin x + cos x + c) \end{matrix}

\frac{d (I + J)}{d x}

x = \sqrt{2}

\int \frac{sin x + cos x}{\sqrt{(1 + sin 2 x)}} d x = x .

$\int \frac{2 s i n x}{(3 + s i n 2 x)} d x$ is equal to

\int \frac{cos (x - a)}{sin x} d x = cos a log | sin x | + x sin a + c

\int \frac{sin (x - a)}{cos (x - b)} d x = cos (b - a) log | sec (x - b) | + x sin (b - a) + c

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