The integral of ∫secx(secx + tanx)dx can be solved using the method of substitution.

Step 1: Let's set u = secx + tanx. Then, du = (secx*tanx + sec^2x)dx.

Step 2: Notice that the integrand is just u*du. So, the integral becomes ∫u du.

Step 3: The integral of u with respect to u is (1/2)u^2.

Step 4: Substituting back for u, we get (1/2)(secx + tanx)^2.

Step 5: Don't forget to add the constant of integration, C.

So, ∫secx(secx + tanx)dx = (1/2)(secx + tanx)^2 + C.

Question

The integral of ∫secx(secx + tanx)dx can be solved using the method of substitution.

Step 1: Let's set u = secx + tanx. Then, du = (secx*tanx + sec^2x)dx.

Step 2: Notice that the integrand is just u*du. So, the integral becomes ∫u du.

Step 3: The integral of u with respect to u is (1/2)u^2.

Step 4: Substituting back for u, we get (1/2)(secx + tanx)^2.

Step 5: Don't forget to add the constant of integration, C.

So, ∫secx(secx + tanx)dx = (1/2)(secx + tanx)^2 + C.

Knowee AI · Accepted Answer

The integral of ∫secx(secx + tanx)dx can be solved using the method of substitution.

Step 1: Let's set u = secx + tanx. Then, du = (secx*tanx + sec^2x)dx.

Step 2: Notice that the integrand is just u*du. So, the integral becomes ∫u du.

Step 3: The integral of u with respect to u is (1/2)u^2.

Step 4: Substituting back for u, we get (1/2)(secx + tanx)^2.

Step 5: Don't forget to add the constant of integration, C.

So, ∫secx(secx + tanx)dx = (1/2)(secx + tanx)^2 + C.

Integration of ∫secxsecx+tanxdx∫sec⁡𝑥sec⁡𝑥+tan⁡𝑥𝑑𝑥 equals: (where C𝐶 is constant of integration)