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

The integral of cos(x)(e^{7sin(x)}) is 1/7 e^{7sin(x)}+C

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

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

\frac{1}{7} e^{7 s i n (x)} + C

Solution steps

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

Apply u-substitution

: \int \frac{e ^{u}}{7} d u

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

Take the constant out:

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

= \frac{1}{7} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{7} e^{u}

Substitute back

u = 7 sin (x)

= \frac{1}{7} e^{7 s i n (x)}

Add a constant to the solution

= \frac{1}{7} e^{7 s i n (x)} + C

\frac{( - 8 x )}{2 x - 1}

y^{^{'}} = \frac{2 x y ^{2} + 8 x}{( x ^{2} y + 3 y )}

x \to 0 + lim ((e^{x} - 1)^{x})

\int t (ln (t))^{2} d t

x \to 0 - lim (\frac{5}{tan ( x )})

What is the integral of cos(x)(e^{7sin(x)}) ?
The integral of cos(x)(e^{7sin(x)}) is 1/7 e^{7sin(x)}+C