What is the integral of e^2cos(3x) ?

The integral of e^2cos(3x) is (e^2)/3 sin(3x)+C

integral of e^2cos(3x)

\int e^{2} cos (3 x) d x

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

Solution steps

\int e^{2} cos (3 x) d x

Take the constant out:

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

= e^{2} \cdot \int cos (3 x) d x

Apply u-substitution

= e^{2} \cdot \int cos (u) \frac{1}{3} d u

Take the constant out:

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

= e^{2} \frac{1}{3} \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= e^{2} \frac{1}{3} sin (u)

Substitute back

u = 3 x

= e^{2} \frac{1}{3} sin (3 x)

Simplify

e^{2} \frac{1}{3} sin (3 x) : \frac{e ^{2}}{3} sin (3 x)

= \frac{e ^{2}}{3} sin (3 x)

Add a constant to the solution

= \frac{e ^{2}}{3} sin (3 x) + C

\frac{d}{d x} (cos (arcsin (3 x)))

\frac{d x}{d t} = 6 - \frac{7 x}{600 + 2 t}

\int \frac{3 x - 5}{x ^{2}} d x

\int \frac{x ^{3} + 23}{x ^{2} + 7 x + 12} d x

d er i v a t i v e y = csc (x) (x + cot (x))

What is the integral of e^2cos(3x) ?
The integral of e^2cos(3x) is (e^2)/3 sin(3x)+C