What is the integral of 1/(sin^2(a)x)+c ?

The integral of 1/(sin^2(a)x)+c is csc^2(a)ln|x|+cx+C

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integral of 1/(sin^2(a)x)+c

\int \frac{1}{sin ^{2} ( a ) x} + c d x

csc^{2} (a) ln ∣ x ∣ + c x + C

Solution steps

\int \frac{1}{sin ^{2} ( a ) x} + c 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 \frac{1}{sin ^{2} ( a ) x} d x + \int c d x

\int \frac{1}{sin ^{2} ( a ) x} d x = csc^{2} (a) ln ∣ x ∣

\int c d x = c x

= csc^{2} (a) ln ∣ x ∣ + c x

Add a constant to the solution

= csc^{2} (a) ln ∣ x ∣ + c x + C

\int \frac{25 x ^{2} - 16}{x ^{4}} d x

y = \frac{2}{3 x ^{4}}

e^{2 x} (2 x + 3)^{7}

\frac{\partial}{\partial t} (x)

x d y = (2 x e^{x} - y + 6 x^{2}) d x

What is the integral of 1/(sin^2(a)x)+c ?
The integral of 1/(sin^2(a)x)+c is csc^2(a)ln|x|+cx+C