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

The integral of e^{sin(x)}*cos(x) is e^{sin(x)}+C

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

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

e^{s i n (x)} + C

Solution steps

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

Apply u-substitution

: \int e^{u} d u

= \int e^{u} d u

Use the common integral:

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

= e^{u}

Substitute back

u = sin (x)

= e^{s i n (x)}

Add a constant to the solution

= e^{s i n (x)} + C

\int \frac{x - 11}{x ^{2} + 3 x - 4} d x

n = 0 \sum \infty \frac{4 ^{n}}{n !}

x \to \infty lim (1. 1^{x})

x \to 1 lim (x^{4} - 3 x^{2} + 6)

x \to - 1 lim (\frac{x ^{3} + x}{1 + x})

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