What is the integral of 7^{cos(x)}sin(x) ?

The integral of 7^{cos(x)}sin(x) is -(7^{cos(x)})/(ln(7))+C

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integral of 7^{cos(x)}sin(x)

\int 7^{c o s (x)} sin (x) d x

- \frac{7 ^{c o s (x)}}{ln ( 7 )} + C

Solution steps

\int 7^{c o s (x)} sin (x) d x

Apply u-substitution

: \int - 7^{u} d u

= \int - 7^{u} d u

Take the constant out:

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

= - \int 7^{u} d u

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

= - \frac{7 ^{u}}{ln ( 7 )}

Substitute back

u = cos (x)

= - \frac{7 ^{c o s (x)}}{ln ( 7 )}

Add a constant to the solution

= - \frac{7 ^{c o s (x)}}{ln ( 7 )} + C

y = x cos (x)

x = 63 - 7 y^{2}, x = 7 y^{2} - 63

t^{3} - t

\frac{d}{d x} (1 - x^{2} - x arccos (x))

y \frac{d y}{d x} = - 8 cos (π x)

What is the integral of 7^{cos(x)}sin(x) ?
The integral of 7^{cos(x)}sin(x) is -(7^{cos(x)})/(ln(7))+C