What is the integral of cos(3θ) ?

The integral of cos(3θ) is 1/3 sin(3θ)+C

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integral of cos(3θ)

\int cos (3 θ) d θ

\frac{1}{3} sin (3 θ) + C

Solution steps

\int cos (3 θ) d θ

Apply u-substitution

: \int cos (u) \frac{1}{3} d u

= \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

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

Use the common integral:

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

= \frac{1}{3} sin (u)

Substitute back

u = 3 θ

= \frac{1}{3} sin (3 θ)

Add a constant to the solution

= \frac{1}{3} sin (3 θ) + C

x \to - 2 lim (\frac{3 x - 6}{x + 2})

\frac{d}{d x} (\frac{x ^{3}}{2 ( x + 1 ) ^{2}})

e^{x}

\int \frac{2 x ^{3} - 6 x ^{2} - 10 x - 6}{x ^{2} - 1} d x

3 y^{^{''}} - y^{^{'}} + 2 y = 0, y (0) = 2, y^{^{'}} (0) = 0