What is the integral of 5^{cos(x)}sin(x) ?

The integral of 5^{cos(x)}sin(x) is -(5^{cos(x)})/(ln(5))+C

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integral of 5^{cos(x)}sin(x)

\int 5^{c o s (x)} sin (x) d x

- \frac{5 ^{c o s (x)}}{ln ( 5 )} + C

Solution steps

\int 5^{c o s (x)} sin (x) d x

Apply u-substitution

: \int - 5^{u} d u

= \int - 5^{u} d u

Take the constant out:

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

= - \int 5^{u} d u

\int a^{x} d x = \frac{a ^{x}}{ln a}

= - \frac{5 ^{u}}{ln ( 5 )}

Substitute back

u = cos (x)

= - \frac{5 ^{c o s (x)}}{ln ( 5 )}

Add a constant to the solution

= - \frac{5 ^{c o s (x)}}{ln ( 5 )} + C

\frac{d}{d y} (2 x^{3} + 6 x y^{2} - 3 x^{2} + 3 y^{2})

\frac{d y}{d x} = \frac{1 + 2 y}{1 + x}

1 + 2 t

\frac{d ^{2}}{d x ^{2}} (\frac{1}{1 + x ^{2}})

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

What is the integral of 5^{cos(x)}sin(x) ?
The integral of 5^{cos(x)}sin(x) is -(5^{cos(x)})/(ln(5))+C