What is the integral of cos^2(1/2)x ?

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

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integral of cos^2(1/2)x

\int cos^{2} (\frac{1}{2}) x d x

\frac{cos ^{2} ( \frac{1}{2} ) x ^{2}}{2} + C

Solution steps

\int cos^{2} (\frac{1}{2}) x d x

Take the constant out:

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

= cos^{2} (\frac{1}{2}) \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= cos^{2} (\frac{1}{2}) \frac{x ^{2}}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{cos ^{2} ( \frac{1}{2} ) x ^{2}}{2}

Add a constant to the solution

= \frac{cos ^{2} ( \frac{1}{2} ) x ^{2}}{2} + C

\frac{3 s}{( s - 1 ) ( s ^{2} - 4 )}

\int \frac{( 6 x - 7 )}{3 x ^{2} - 7 x + 11} d x

(2, - 3), (- 1, 15)

\frac{\partial}{\partial x} (x^{5} + 3 x^{3} y^{2} + 3 x y^{4})

x \to 1 lim (\frac{x ^{2}}{x - 1})

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