What is the integral of cos^2(t) ?

The integral of cos^2(t) is 1/2 (t+1/2 sin(2t))+C

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integral of cos^2(t)

\int cos^{2} (t) d t

\frac{1}{2} (t + \frac{1}{2} sin (2 t)) + C

Solution steps

\int cos^{2} (t) d t

Rewrite using trig identities

= \int \frac{1 + cos ( 2 t )}{2} d t

Take the constant out:

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

= \frac{1}{2} \cdot \int 1 + cos (2 t) d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int 1 d t + \int cos (2 t) d t)

\int 1 d t = t

\int cos (2 t) d t = \frac{1}{2} sin (2 t)

= \frac{1}{2} (t + \frac{1}{2} sin (2 t))

Add a constant to the solution

= \frac{1}{2} (t + \frac{1}{2} sin (2 t)) + C

\int - 2 sin (2 t + 7) d t

3 sec (x), at x = \frac{π}{6}

\int_{0}^{3} x^{4} d x

y^{^{''}} - 4 y = 24 t e^{(- 2 t)} + 2 e^{(- 2 t)} + 8 - 8 t

x \to 4 lim (x^{2} + 5 x)

What is the integral of cos^2(t) ?
The integral of cos^2(t) is 1/2 (t+1/2 sin(2t))+C