What is the integral of e^{cos(25t)}sin(25t) ?

The integral of e^{cos(25t)}sin(25t) is -1/25 e^{cos(25t)}+C

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integral of e^{cos(25t)}sin(25t)

\int e^{c o s (25 t)} sin (25 t) d t

- \frac{1}{25} e^{c o s (25 t)} + C

Solution steps

\int e^{c o s (25 t)} sin (25 t) d t

Apply u-substitution

: \int e^{c o s (u)} sin (u) \frac{1}{25} d u

= \int e^{c o s (u)} sin (u) \frac{1}{25} d u

Take the constant out:

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

= \frac{1}{25} \cdot \int e^{c o s (u)} sin (u) d u

Apply u-substitution

: \int - e^{v} d v

= \frac{1}{25} \cdot \int - e^{v} d v

Take the constant out:

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

= \frac{1}{25} (- \int e^{v} d v)

Use the common integral:

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

= \frac{1}{25} (- e^{v})

Substitute back

= \frac{1}{25} (- e^{c o s (25 t)})

Simplify

= - \frac{1}{25} e^{c o s (25 t)}

Add a constant to the solution

= - \frac{1}{25} e^{c o s (25 t)} + C

x + \frac{5}{x}

\frac{x d y}{d x} - y = x^{2017} \cdot y^{2}

\frac{\partial}{\partial x} ((2 - x y) e^{- x y})

\frac{\partial}{\partial x} ((2 x + 2 y) e^{y})

\int \frac{2 y}{x ^{2} + 1} d y

What is the integral of e^{cos(25t)}sin(25t) ?
The integral of e^{cos(25t)}sin(25t) is -1/25 e^{cos(25t)}+C