We use the following formula for integration:

We have the following integral:
![\int(15x^2+\frac{\sqrt[3]{x^2}}{4})dx](https://img.qammunity.org/2023/formulas/mathematics/college/2ly3l4fonfm8e4peozr48460swl1jbq68h.png)
Separate into two integrals:
![\int(15x^2+\frac{\sqrt[3]{x^2}}{4})dx=\int15x^2dx+\int\frac{\sqrt[3]{x^2}}{4}dx](https://img.qammunity.org/2023/formulas/mathematics/college/36awb4ryopdqw1xep3xsuwgal7l9mo2c1q.png)
Calculate the first integral. Take the coefficient out of the integral:

Apply the integration formula:

Calculate the second integral. Take the coefficient out of the integral:
![\int\frac{\sqrt[3]{x^2}}{4}dx=(1)/(4)\int\sqrt[3]{x^2}dx](https://img.qammunity.org/2023/formulas/mathematics/college/ctpv0dni7clrybifk2q9mhobldcgh1wpak.png)
Express the radical as a fractional exponent:
![(1)/(4)\int\sqrt[3]{x^2}dx=(1)/(4)\int x^(2/3)dx](https://img.qammunity.org/2023/formulas/mathematics/college/nqsw7dofehonxpdr2jsytg0fsnsij7tzlp.png)
Apply the integration formula:
![(1)/(4)\cdot(x^(5/3))/(5/3)+C=(3)/(20)\sqrt[3]{x^5}+C](https://img.qammunity.org/2023/formulas/mathematics/college/kyd20msbfmehk4jatpw4bu88064g6wj7mw.png)
The total integral is:
![\int(15x^2+\frac{\sqrt[3]{x^2}}{4})dx=5x^3+(3)/(20)\sqrt[3]{x^5}+C](https://img.qammunity.org/2023/formulas/mathematics/college/14h6ienw8fdh452kzwy4yaerq3yrolziys.png)