What is the integral of 3*cos(3x) ?

The integral of 3*cos(3x) is sin(3x)+C

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integral of 3*cos(3x)

\int 3 \cdot cos (3 x) d x

sin (3 x) + C

Solution steps

\int 3 cos (3 x) d x

Take the constant out:

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

= 3 \cdot \int cos (3 x) d x

Apply u-substitution

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

= 3 \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

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

Use the common integral:

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

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

Substitute back

u = 3 x

= 3 \cdot \frac{1}{3} sin (3 x)

Simplify

3 \cdot \frac{1}{3} sin (3 x) : sin (3 x)

= sin (3 x)

Add a constant to the solution

= sin (3 x) + C

\int \frac{x ^{15}}{x ^{16} + 1} d x

\int 2 x (x^{2} + 2)^{7} d x

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

10 x^{2}

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