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Nadya [2.5K]
3 years ago
11

Evaluate the indefinite integral. (Use C for the constant of integration.) sin(10x) 1 cos2(10x) dx

Mathematics
1 answer:
Schach [20]3 years ago
5 0

Answer:

The result of the integral is -\frac{\cos^3{10x}}{30} + C

Step-by-step explanation:

We are given the following integral:

\int \sin{(10x)}\cos^{2}{(10x)} dx

I am going to solve by substitution, using u = \cos{10x}, so du = -10\sin{10x}dx, dx = -\frac{du}{10\sin{10x}}. So, we have

-\frac{1}{10} \int u^2 du

Which has the following result:

-\frac{u^3}{30} + C

Going back to x, the result of the integral is

-\frac{\cos^3{10x}}{30} + C

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