What is the integral of (cos(5/2)x)^4 ?

The integral of (cos(5/2)x)^4 is (cos^4(5/2)x^5)/5+C

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integral of (cos(5/2)x)^4

\int (cos (\frac{5}{2}) x)^{4} d x

\frac{cos ^{4} ( \frac{5}{2} ) x ^{5}}{5} + C

Solution steps

\int (cos (\frac{5}{2}) x)^{4} d x

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= \int cos^{4} (\frac{5}{2}) x^{4} d x

Take the constant out:

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

= cos^{4} (\frac{5}{2}) \cdot \int x^{4} d x

Apply the Power Rule

: \frac{x ^{5}}{5}

= cos^{4} (\frac{5}{2}) \frac{x ^{5}}{5}

Multiply fractions:

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

= \frac{cos ^{4} ( \frac{5}{2} ) x ^{5}}{5}

Add a constant to the solution

= \frac{cos ^{4} ( \frac{5}{2} ) x ^{5}}{5} + C

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What is the integral of (cos(5/2)x)^4 ?
The integral of (cos(5/2)x)^4 is (cos^4(5/2)x^5)/5+C