calculate the indefinite integral (cosx)/(sin^3x)

nevermind i found the answer

Too bad :( I knew it too :)

To calculate the indefinite integral of (cosx)/(sin^3x), we can use a u-substitution.

Let's start by letting u = sinx. Then, we can take the derivative of u to find du/dx, which is equal to cosx.

Now, rearrange the original integral and substitute u and du/dx into the integral:

∫(cosx)/(sin^3x) dx = ∫(1/u^3)(du/dx) dx

Since du/dx = cosx, we can simplify the integral to:

∫(1/u^3) cosx dx

Next, we can simplify further by using the power rule for integration:

∫(1/u^3) cosx dx = ∫u^-3 cosx dx

Now, we have an integrand that can be rewritten as a product of two functions: u^-3 and cosx.

To integrate u^-3, we can add 1 to the exponent and divide the resulting term by the new exponent:

∫u^-3 cosx dx = (u^-2 / -2) + C

Finally, substituting u back in as sinx:

∫(cosx)/(sin^3x) dx = (-sin^2x / 2) + C

Therefore, the indefinite integral of (cosx)/(sin^3x) is (-sin^2x / 2) + C, where C is the constant of integration.