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

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

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

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

\frac{3 x ^{2}}{2} + C

Solution steps

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

Rewrite using trig identities

= 3 \cdot \int x d x

Apply the Power Rule

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

= 3 \cdot \frac{x ^{2}}{2}

Multiply fractions:

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

= \frac{3 x ^{2}}{2}

Add a constant to the solution

= \frac{3 x ^{2}}{2} + C

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