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

The integral of e^{sin(x)}7cos(x) is 7e^{sin(x)}+C

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

\int e^{s i n (x)} 7 cos (x) d x

7 e^{s i n (x)} + C

Solution steps

\int e^{s i n (x)} \cdot 7 cos (x) d x

Take the constant out:

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

= 7 \cdot \int e^{s i n (x)} cos (x) d x

Apply u-substitution

: \int e^{u} d u

= 7 \cdot \int e^{u} d u

Use the common integral:

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

= 7 e^{u}

Substitute back

u = sin (x)

= 7 e^{s i n (x)}

Add a constant to the solution

= 7 e^{s i n (x)} + C

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

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

x \to 0 + lim (x ln (x^{5}))

\frac{d}{d x} (\frac{x + 3}{2 x ^{2} e ^{x}})

x^{2} + y^{2} = 27, at x = 3

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