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

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

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integral of e^{sin(t)}cos(t)

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

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

Solution steps

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

Apply u-substitution

= \int e^{u} d u

Use the common integral:

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

= e^{u}

Substitute back

u = sin (t)

= e^{s i n (t)}

Add a constant to the solution

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

\int \frac{( x + 4 ) ^{4}}{2 x} d x

\frac{d}{d x} ((3 x^{2} - 13)^{3})

\frac{d}{d x} (\frac{sin ( x )}{y ^{2}})

\frac{d}{d x} (3 \cdot ln (x))

\frac{d}{d x} (- 7 x)

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