Final answer to the problem
$x-\frac{1}{4}\cos\left(2x\right)+C_0$
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Step-by-step Solution
Specify the solving method
1
Find the integral
$\int\frac{\cos\left(x\right)^3-\sin\left(x\right)^3}{\cos\left(x\right)-\sin\left(x\right)}dx$
Learn how to solve classify algebraic expressions problems step by step online.
$\int\frac{\cos\left(x\right)^3-\sin\left(x\right)^3}{\cos\left(x\right)-\sin\left(x\right)}dx$
Learn how to solve classify algebraic expressions problems step by step online. Integrate the function (cos(x)^3-sin(x)^3)/(cos(x)-sin(x)). Find the integral. Rewrite the trigonometric expression \frac{\cos\left(x\right)^3-\sin\left(x\right)^3}{\cos\left(x\right)-\sin\left(x\right)} inside the integral. Expand the integral \int\left(1+\frac{\sin\left(2x\right)}{2}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int1dx results in: x.
Final answer to the problem
$x-\frac{1}{4}\cos\left(2x\right)+C_0$