Find the indefinite integral.

Question

Find the indefinite integral. ​  ​

Quizplus · Accepted Answer

The integral consists of the function 11eac44f_ecec_e5c2_bedf_835a9cc4e9e1_TB7497_11 and the differential dx, so we need to find the antiderivative of the function with respect to x.

Notice that the function 11eac44f_ecec_e5c2_bedf_835a9cc4e9e1_TB7497_11 is in the form of the derivative of e^(ax). Specifically, the derivative of e^(5x) is 5e^(5x).

Therefore, we can guess that the antiderivative of 11eac44f_ecec_e5c2_bedf_835a9cc4e9e1_TB7497_11 is some constant times e^(5x). Taking the derivative of this guess, we get 5ce^(5x), where c is a constant. This matches the original function, except for the constant factor of 11.

Thus, the antiderivative of the function is (11/5)e^(5x), and the answer is B.

Find the Indefinite Integral. ​ ​

Find the Indefinite Integral.