What is the integral of cos(2x)e^{sin(2x)} ?

The integral of cos(2x)e^{sin(2x)} is 1/2 e^{sin(2x)}+C

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integral of cos(2x)e^{sin(2x)}

\int cos (2 x) e^{s i n (2 x)} d x

\frac{1}{2} e^{s i n (2 x)} + C

Solution steps

\int cos (2 x) e^{s i n (2 x)} d x

Apply u-substitution

: \int cos (u) e^{s i n (u)} \frac{1}{2} d u

= \int cos (u) e^{s i n (u)} \frac{1}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int cos (u) e^{s i n (u)} d u

Apply u-substitution

: \int e^{v} d v

= \frac{1}{2} \cdot \int e^{v} d v

Use the common integral:

\int e^{v} d v = e^{v}

= \frac{1}{2} e^{v}

Substitute back

= \frac{1}{2} e^{s i n (2 x)}

Add a constant to the solution

= \frac{1}{2} e^{s i n (2 x)} + C

y = x^{3} - 3 x + 1, (2, 3)

\frac{d}{d x} (\frac{3 x - 10}{7 x + 13})

f (x) = - \frac{4}{3} x^{- \frac{5}{2}}

\int \frac{9 x ^{2} + 4}{x ^{2}} d x

2 x y - 9 x^{2} + (2 y + x^{2} + 1) \frac{d y}{d x} = 0, y (0) = 3

What is the integral of cos(2x)e^{sin(2x)} ?
The integral of cos(2x)e^{sin(2x)} is 1/2 e^{sin(2x)}+C