Integrate the function $\sin\left(x\right)\ln\left(\sqrt{4-\cos\left(x\right)}\right)-x^2e^x+3x^2$ from $-2$ to $2$

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Learn how to solve problems step by step online. Integrate the function sin(x)ln((4-cos(x))^(1/2))-x^2e^x3x^2 from -2 to 2. Expand the integral \int_{-2}^{2}\left(\sin\left(x\right)\ln\left(\sqrt{4-\cos\left(x\right)}\right)-x^2e^x+3x^2\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{-2}^{2}\sin\left(x\right)\ln\left(\sqrt{4-\cos\left(x\right)}\right)dx results in: 2\left(\left(4-\cos\left(2\right)\right)\frac{1}{4}\ln\left(4-\cos\left(2\right)\right)+\left(4-\cos\left(-2\right)\right)-\frac{1}{4}\ln\left(4-\cos\left(-2\right)\right)\right)-2\left(\left(4-\cos\left(2\right)\right)\frac{1}{4}+\left(4-\cos\left(-2\right)\right)-\frac{1}{4}\right). The integral \int_{-2}^{2}-x^2e^xdx results in: -2\cdot e^2+4\cdot e^{-2}+4\cdot e^{-2}+2\cdot e^{-2}. Gather the results of all integrals.