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

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

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integral of x+2/(sin^2(x))

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

\frac{x ^{2}}{2} - 2 cot (x) + C

Solution steps

\int x + \frac{2}{sin ^{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

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

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

\int \frac{2}{sin ^{2} ( x )} d x = - 2 cot (x)

= \frac{x ^{2}}{2} - 2 cot (x)

Add a constant to the solution

= \frac{x ^{2}}{2} - 2 cot (x) + C

y^{^{''}} - y = 0, y (0) = 0, y^{^{'}} (0) = 1

\frac{d}{d x} (8 cos^{4} (x))

x \to - 1 lim (f (x))

1. 1^{x} + 9^{x} d x

\frac{40}{x ^{9}}

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