What is the integral of e^{4sin(x)}cos(x) ?

The integral of e^{4sin(x)}cos(x) is 1/4 e^{4sin(x)}+C

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integral of e^{4sin(x)}cos(x)

\int e^{4 s i n (x)} cos (x) d x

\frac{1}{4} e^{4 s i n (x)} + C

Solution steps

\int e^{4 s i n (x)} cos (x) d x

Apply u-substitution

: \int \frac{e ^{u}}{4} d u

= \int \frac{e ^{u}}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{4} e^{u}

Substitute back

u = 4 sin (x)

= \frac{1}{4} e^{4 s i n (x)}

Add a constant to the solution

= \frac{1}{4} e^{4 s i n (x)} + C

\int (x + 3)^{- \frac{1}{2}} d x

z e^{z}

\frac{\partial}{\partial x} ((x^{2} - 1) \cdot (y + 2))

x \to - 8 - lim (x^{2} - 64)

n = 1 \sum \infty 4^{n + 1} 5^{- n}

What is the integral of e^{4sin(x)}cos(x) ?
The integral of e^{4sin(x)}cos(x) is 1/4 e^{4sin(x)}+C