Exercise
$\int x\left(5x^{\frac{2}{5}}+6x^{\frac{1}{2}}+3x+2\right)dx$
Step-by-step Solution
Learn how to solve problems step by step online. Integrate int(x(5x^(2/5)+6x^(1/2)3x+2))dx. Rewrite the integrand x\left(5\sqrt[5]{x^{2}}+6\sqrt{x}+3x+2\right) in expanded form. Expand the integral \int\left(5\sqrt[5]{x^{7}}+6\sqrt{x^{3}}+3x^2+2x\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int5\sqrt[5]{x^{7}}dx results in: \frac{25\sqrt[5]{x^{12}}}{12}. The integral \int6\sqrt{x^{3}}dx results in: \frac{12\sqrt{x^{5}}}{5}.
Integrate int(x(5x^(2/5)+6x^(1/2)3x+2))dx
Final answer to the exercise
$\frac{25\sqrt[5]{x^{12}}}{12}+\frac{12\sqrt{x^{5}}}{5}+x^{3}+x^2+C_0$