Final answer to the problem
$\frac{5}{6}x^{6}-\frac{2}{3}\ln\left|x\right|+\frac{3}{5}e^{-5x}+2\sqrt{x}+\frac{5}{2}\sin\left(2x\right)+C_0$
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Step-by-step Solution
Learn how to solve problems step by step online. Find the integral int(5x^5+-2/(3x)-3e^(-5x)1/(x^(1/2))5cos(2x))dx. Expand the integral \int\left(5x^5+\frac{-2}{3x}-3e^{-5x}+\frac{1}{\sqrt{x}}+5\cos\left(2x\right)\right)dx into 5 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int5x^5dx results in: \frac{5}{6}x^{6}. The integral \int\frac{-2}{3x}dx results in: -\frac{2}{3}\ln\left(x\right). The integral \int-3e^{-5x}dx results in: \frac{3}{5}e^{-5x}.
Final answer to the problem
$\frac{5}{6}x^{6}-\frac{2}{3}\ln\left|x\right|+\frac{3}{5}e^{-5x}+2\sqrt{x}+\frac{5}{2}\sin\left(2x\right)+C_0$
