What is the integral of 4sin(4t) ?

The integral of 4sin(4t) is -cos(4t)+C

Popular >

integral of 4sin(4t)

\int 4 sin (4 t) d t

- cos (4 t) + C

Solution steps

\int 4 sin (4 t) d t

Take the constant out:

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

= 4 \cdot \int sin (4 t) d t

Apply u-substitution

: \int sin (u) \frac{1}{4} d u

= 4 \cdot \int sin (u) \frac{1}{4} d u

Take the constant out:

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

= 4 \cdot \frac{1}{4} \cdot \int sin (u) d u

Use the common integral:

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

= 4 \cdot \frac{1}{4} (- cos (u))

Substitute back

u = 4 t

= 4 \cdot \frac{1}{4} (- cos (4 t))

Simplify

4 \cdot \frac{1}{4} (- cos (4 t)) : - cos (4 t)

= - cos (4 t)

Add a constant to the solution

= - cos (4 t) + C

\int e^{t^{2}} t d t

\int \frac{( x ^{2} - 2 x + 11 )}{( x ^{2} + 3 x - 4 )} d x

\int (8 x^{4} - 5 x^{2} + 2) d x

\int \frac{x ^{\frac{1}{2}}}{x} d x

\int \frac{2}{4 + 9 x ^{2}} d x