What is the integral of-10e^{cos(x)}sin(x) ?

The integral of-10e^{cos(x)}sin(x) is 10e^{cos(x)}+C

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integral of-10e^{cos(x)}sin(x)

\int - 10 e^{c o s (x)} sin (x) d x

10 e^{c o s (x)} + C

Solution steps

\int - 10 e^{c o s (x)} sin (x) d x

Take the constant out:

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

= - 10 \cdot \int e^{c o s (x)} sin (x) d x

Apply u-substitution

: \int - e^{u} d u

= - 10 \cdot \int - e^{u} d u

Take the constant out:

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

= - 10 (- \int e^{u} d u)

Use the common integral:

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

= - 10 (- e^{u})

Substitute back

u = cos (x)

= - 10 (- e^{c o s (x)})

Simplify

= 10 e^{c o s (x)}

Add a constant to the solution

= 10 e^{c o s (x)} + C

f^{^{'}} (x) = 2 x

\int cos^{2} (\frac{4 - x}{3}) d x

\frac{d}{d t} (\frac{1}{2} t)

\int x^{2} (x^{3} + 9)^{7} d x

f (x) = x^{\frac{7}{5}} (x + 5)

What is the integral of-10e^{cos(x)}sin(x) ?
The integral of-10e^{cos(x)}sin(x) is 10e^{cos(x)}+C