What is the integral of 2xsin^2(x)+2xcos^2(x) ?

The integral of 2xsin^2(x)+2xcos^2(x) is x^2+C

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integral of 2xsin^2(x)+2xcos^2(x)

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

x^{2} + C

Solution steps

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

Simplify

2 x sin^{2} (x) + 2 x cos^{2} (x) : 2 x

= \int 2 x d x

Take the constant out:

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

= 2 \cdot \int x d x

Apply the Power Rule

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

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

Simplify

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

= x^{2}

Add a constant to the solution

= x^{2} + C

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What is the integral of 2xsin^2(x)+2xcos^2(x) ?
The integral of 2xsin^2(x)+2xcos^2(x) is x^2+C