Exercise
$\int\frac{x^3\left(1-x\right)}{\sqrt{x+1}}dx$
Step-by-step Solution
Learn how to solve problems step by step online. Find the integral int((x^3(1-x))/((x+1)^(1/2)))dx. Multiply the single term x^3 by each term of the polynomial \left(1-x\right). When multiplying exponents with same base you can add the exponents: -x\cdot x^3. Expand the fraction \frac{x^3-x^{4}}{\sqrt{x+1}} into 2 simpler fractions with common denominator \sqrt{x+1}. Simplify the expression.
Find the integral int((x^3(1-x))/((x+1)^(1/2)))dx
Final answer to the exercise
$-4\sqrt{x+1}-\frac{18}{5}\sqrt{\left(x+1\right)^{5}}+\frac{10}{7}\sqrt{\left(x+1\right)^{7}}+\frac{14}{3}\sqrt{\left(x+1\right)^{3}}+\frac{-2\sqrt{\left(x+1\right)^{9}}}{9}+C_0$