What is the integral of 3sin(t) ?

The integral of 3sin(t) is -3cos(t)+C

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integral of 3sin(t)

\int 3 sin (t) d t

- 3 cos (t) + C

Solution steps

\int 3 sin (t) d t

Take the constant out:

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

= 3 \cdot \int sin (t) d t

Use the common integral:

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

= 3 (- cos (t))

Simplify

= - 3 cos (t)

Add a constant to the solution

= - 3 cos (t) + C

\int x \cdot (sin (x))^{2} d x

\int 3 sin^{2} (t) d t

y^{^{'''}} + 6 y^{^{''}} + 11 y^{^{'}} + 6 y = 0

\int \frac{e ^{2 x} + e ^{4 x}}{e ^{x} - e ^{5 x}} d x

(9 y^{2} - x y) d x + (x^{2}) d y = 0