What is the integral of e^{cos^2(x)}sin(x)cos(x) ?

The integral of e^{cos^2(x)}sin(x)cos(x) is -1/2 e^{cos^2(x)}+C

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integral of e^{cos^2(x)}sin(x)cos(x)

\int e^{c o s^{2} (x)} sin (x) cos (x) d x

- \frac{1}{2} e^{c o s^{2} (x)} + C

Solution steps

\int e^{c o s^{2} (x)} sin (x) cos (x) d x

Apply u-substitution

: \int - e^{u^{2}} u d u

= \int - e^{u^{2}} u d u

Take the constant out:

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

= - \int e^{u^{2}} u d u

Apply u-substitution

: \int \frac{e ^{v}}{2} d v

= - \int \frac{e ^{v}}{2} d v

Take the constant out:

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

= - \frac{1}{2} \cdot \int e^{v} d v

Use the common integral:

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

= - \frac{1}{2} e^{v}

Substitute back

= - \frac{1}{2} e^{c o s^{2} (x)}

Add a constant to the solution

= - \frac{1}{2} e^{c o s^{2} (x)} + C

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What is the integral of e^{cos^2(x)}sin(x)cos(x) ?
The integral of e^{cos^2(x)}sin(x)cos(x) is -1/2 e^{cos^2(x)}+C