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

The integral of cos(2)x^2 is 1/3 cos(2)x^3+C

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integral of cos(2)x^2

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

\frac{1}{3} cos (2) x^{3} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

: \frac{x ^{3}}{3}

= cos (2) \frac{x ^{3}}{3}

Simplify

cos (2) \frac{x ^{3}}{3} : \frac{1}{3} cos (2) x^{3}

= \frac{1}{3} cos (2) x^{3}

Add a constant to the solution

= \frac{1}{3} cos (2) x^{3} + C

f (x) = \frac{7}{x}, at x = 6

y^{^{'}} = \frac{e ^{x} - e ^{y}}{1 + e ^{x}}

\int \frac{sin ( 2 x )}{12 + cos ^{2} ( x )} d x

\frac{2}{( s ^{3} - 7 s ^{2} + 2 s + 40 )}

arccos (∣ x + 1 ∣)

What is the integral of cos(2)x^2 ?
The integral of cos(2)x^2 is 1/3 cos(2)x^3+C