Exercise
$\int\frac{\left(1-\sqrt{x}\right)}{\sqrt[4]{x}}dx$
Step-by-step Solution
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((1-x^(1/2))/(x^(1/4)))dx. Expand the fraction \frac{1-\sqrt{x}}{\sqrt[4]{x}} into 2 simpler fractions with common denominator \sqrt[4]{x}. Simplify the resulting fractions. Expand the integral \int\left(\frac{1}{\sqrt[4]{x}}-\sqrt[4]{x}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{\sqrt[4]{x}}dx results in: \frac{4\sqrt[4]{x^{3}}}{3}.
Find the integral int((1-x^(1/2))/(x^(1/4)))dx
Final answer to the exercise
$\frac{4\sqrt[4]{x^{3}}}{3}+\frac{-4\sqrt[4]{x^{5}}}{5}+C_0$