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)

integral

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

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

\int \frac{4 x - 5}{x ^{2} + 8 x + 7} d x

\int \frac{2}{x} d x

\int \frac{3}{2 x + 1} d x

\int \frac{1}{8} x^{3} d x

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