What is the integral of cos(4)(x) ?

The integral of cos(4)(x) is 1/2 cos(4)x^2+C

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integral of cos(4)(x)

\int cos (4) (x) d x

\frac{1}{2} cos (4) x^{2} + C

Solution steps

\int cos (4) x d x

Take the constant out:

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

= cos (4) \cdot \int x d x

Apply the Power Rule

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

= cos (4) \frac{x ^{2}}{2}

Simplify

cos (4) \frac{x ^{2}}{2} : \frac{1}{2} cos (4) x^{2}

= \frac{1}{2} cos (4) x^{2}

Add a constant to the solution

= \frac{1}{2} cos (4) x^{2} + C

\int \frac{1}{( x ( 1 + x ) )} d x

6 x^{2}

\int x^{2} (x^{3} + 4)^{- \frac{1}{2}} d x

\int 2 cos (x) + \frac{5}{x} d x

\int \frac{1}{x} - \frac{5}{16 x ^{2} + 1} d x

What is the integral of cos(4)(x) ?
The integral of cos(4)(x) is 1/2 cos(4)x^2+C