Question

integration of cos^3x​

Answer 1

Answer: Cos3x=4cos^3(X)-3cos (X). Therefore cos^3(x)=(cos3x+3cosx)/4.

Step-by-step explanation:

Substitute this value and can continue the integration.

Answer 2

$\int \: {cos}^{3} xdx \\ \\ = \int \: \frac{1}{4} (cos3x + 3cosx)dx \\ \\ = \frac{1}{4} \int \:cos3x \: dx + \frac{3}{4} \int \: cosx \: dx \\ \\ = \frac{1}{4} \frac{sin3x}{3} + \frac{3}{4} sinx + c \\ \\ = \frac{1}{12} sin3x + \frac{3}{4} sinx + c$