What is the integral of sin(bx) ?

The integral of sin(bx) is -1/b cos(bx)+C

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integral of sin(bx)

\int sin (b x) d x

- \frac{1}{b} cos (b x) + C

Solution steps

\int sin (b x) d x

Apply u-substitution

: \int \frac{sin ( u )}{b} d u

= \int \frac{sin ( u )}{b} d u

Take the constant out:

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

= \frac{1}{b} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{b} (- cos (u))

Substitute back

u = b x

= \frac{1}{b} (- cos (b x))

Simplify

= - \frac{1}{b} cos (b x)

Add a constant to the solution

= - \frac{1}{b} cos (b x) + C

\frac{1}{( s - 3 ) ^{2}}

\int \frac{2 cos ( x )}{5 + sin ^{2} ( x )} d x

\int 70 x e^{7 x^{2}} d x

x \to 0 lim (\frac{2 - x}{x})

sec (3 x)