What is the integral of cos^5(x ?

The integral of cos^5(x is (x^2cos^5(d))/2+C

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integral of cos^5(x

\int cos^{5} (d) x d x

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

Solution steps

\int cos^{5} (d) x d x

Take the constant out:

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

= cos^{5} (d) \cdot \int x d x

Apply the Power Rule

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

= cos^{5} (d) \frac{x ^{2}}{2}

Multiply fractions:

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

= \frac{x ^{2} cos ^{5} ( d )}{2}

Add a constant to the solution

= \frac{x ^{2} cos ^{5} ( d )}{2} + C

\int \frac{10}{1 - sin ^{2} ( x )} d x

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

\int \frac{2 x ^{3} + 5 x ^{2} - 2 x}{x} d x

x \to 0 lim (cos (5 x))

r (t) - 4 tan (5 t^{3})