Integral of csc(x): A step-by-step guide using substitution method

∫csc(x)dx

To evaluate the integral ∫csc(x)dx, we can use a substitution method

To evaluate the integral ∫csc(x)dx, we can use a substitution method. Let’s start by making the substitution u = cos(x).

Differentiating both sides with respect to x, we get du = -sin(x)dx.

Now, let’s solve for dx in terms of du:
dx = -du/sin(x).

Next, we substitute these values into the original integral:
∫csc(x)dx = ∫csc(x) * (-du/sin(x)).

Simplifying this expression, we have:
∫-du = -u + C.

Finally, substituting back u = cos(x), we get:
∫csc(x)dx = -cos(x) + C.

Therefore, the indefinite integral of csc(x)dx is -cos(x) + C (where C is the constant of integration).

More Answers: