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

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

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integral of cos^2(a)x

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Multiply fractions:

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

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

Add a constant to the solution

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

\int_{1}^{\infty} \frac{x}{x ^{2} + 3} d x

\int 1 - 16 x^{2} d x

arcsin (\frac{x}{2})

\frac{d y}{d x} = \frac{2 x}{x + 2}

\int \frac{12}{x ^{5}} d x

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