(P1T4Q2) Integration By Parts [CLASS//QUIZIZZ]

$$\left(\ln\left(x\right)\right)\left(\frac{x^4}{4}\right)-\int\left(\frac{x^4}{4}\right)\left(\frac{1}{x}dx\right)$$

$$\left(\ln\left(x\right)\right)\left(x^3\right)-\int\left(\frac{1}{x}\right)\left(\frac{x^2}{2}dx\right)$$

$$\frac{x^4\cdot\ln\left(x\right)}{4}-\frac{1}{4}\int x^4dx$$

$$\frac{x^4-\ln\left(x\right)}{4}-4\int x^4dx$$

$$\frac{x^4\cdot\ln\left(x\right)}{4}-\frac{1}{4}\left(\frac{x^5}{5}+C\right)$$

$$\frac{x^4\cdot\ln\left(x\right)}{4}-\frac{1}{4}\left(4x^3+C\right)$$

$$\left(8x\right)\left(\frac{\sin\left(2x\right)}{2}\right)-\int\left(\frac{\sin\left(2x\right)}{2}\right)\left(8dx\right)$$

$$\left(8\right)\left(\frac{\sin\left(2x\right)}{2}\right)-\int\left(\frac{\sin\left(2x\right)}{2}\right)\left(8xdx\right)$$

$$4x\cdot\sin\left(2x\right)-4\int\sin\left(2x\right)dx$$

$$4x\cdot\sin\left(2x\right)+4x\int\cos\left(2x\right)dx$$

$$4x\cdot\sin\left(2x\right)-4\left(-\frac{\cos\left(2x\right)}{2}+C\right)$$

$$4x\cdot\sin\left(2x\right)-4\left(\frac{\cos\left(2x\right)}{2}+C\right)$$