Final answer to the problem
Step-by-step Solution
Specify the solving method
Find the integral
Learn how to solve integral calculus problems step by step online.
$\int\left(-\sin\left(x\right)+\cos\left(x\right)+2\right)\left(-\cos\left(x\right)-\sin\left(x\right)\right)dx$
Learn how to solve integral calculus problems step by step online. Integrate the function (-sin(x)+cos(x)+2)(-cos(x)-sin(x)). Find the integral. Rewrite the integrand \left(-\sin\left(x\right)+\cos\left(x\right)+2\right)\left(-\cos\left(x\right)-\sin\left(x\right)\right) in expanded form. Expand the integral \int\left(-\cos\left(2x\right)-2\cos\left(x\right)-2\sin\left(x\right)\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int-\cos\left(2x\right)dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that 2x it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.