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

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

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integral of (x+2)sin^2(2θ)

\int (x + 2) sin^{2} (2 θ)

sin^{2} (2 θ) (2 x + \frac{x ^{2}}{2}) + C

Solution steps

\int (x + 2) sin^{2} (2 θ) d x

Take the constant out:

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

= sin^{2} (2 θ) \cdot \int 2 + x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int 2 d x = 2 x

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

= sin^{2} (2 θ) (2 x + \frac{x ^{2}}{2})

Add a constant to the solution

= sin^{2} (2 θ) (2 x + \frac{x ^{2}}{2}) + C

x \to 0 lim (\frac{4 x ^{2} - 3 x}{x ^{2} + 0.8 x + \frac{4}{x}})

(\frac{x + 8}{x - 8})^{5}

e^{x} ln (x)

n = 1 \sum \infty \frac{1}{n ^{2} + 7 n}

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