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

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

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

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

- cot (x) (2 + 3 cos (x)) - 3 sin (x) + C

Solution steps

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

Apply Integration By Parts

: - cot (x) (2 + 3 cos (x)) - \int 3 sin (x) cot (x) d x

= - cot (x) (2 + 3 cos (x)) - \int 3 sin (x) cot (x) d x

\int 3 sin (x) cot (x) d x = 3 sin (x)

= - cot (x) (2 + 3 cos (x)) - 3 sin (x)

Add a constant to the solution

= - cot (x) (2 + 3 cos (x)) - 3 sin (x) + C

\int \frac{1}{20 + 8 x - x ^{2}} d x

\int_{0}^{2} 2 x d x

\frac{s + 5}{s ^{2} + 6 s + 18}

y^{^{''}} - 6 y^{^{'}} + 9 y = 6 x^{2} + 2 - 12 e^{3 x}

(3 + sin (2 x))^{2}, at x = 0

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