What is the integral of 3x^2(cos^2(x)+sin^2(x)) ?

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

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integral of 3x^2(cos^2(x)+sin^2(x))

\int 3 x^{2} (cos^{2} (x) + sin^{2} (x)) d x

x^{3} + C

Solution steps

\int 3 x^{2} (cos^{2} (x) + sin^{2} (x)) d x

Take the constant out:

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

= 3 \cdot \int x^{2} (cos^{2} (x) + sin^{2} (x)) d x

Rewrite using trig identities

= 3 \cdot \int x^{2} d x

Apply the Power Rule

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

= 3 \cdot \frac{x ^{3}}{3}

Simplify

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

= x^{3}

Add a constant to the solution

= x^{3} + C

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