Evaluate the indefinite integral. (Use $c$ for the constant of integration.) $\int x(x^2+x+2)dx$

Evaluate the indefinite integral as an infinite series: $\int arctan\left(x^4\right) dx$

Evaluate the integral. (Use c for the constant of integration.) ${\int }_{}^{}{(\ln x)}^{2}dx$

Find the general indefinite integral. (Use c for the constant of integration.) $4x^5 \int dx$

Evaluate the indefinite integral as an infinite series: ${\int }_{}^{}\frac{(cosx-1)}{x}dx$.

Evaluate the indefinite integral: $\int (9x^2+81)dx$

Evaluate the integral: ${\int }_0^{\frac{\pi }{2}}9{\cos }^2\left(x\right) dx$.

Evaluate the integral. (Use c for the constant of integration.) $\int 9{\sin }^2\left(x\right){\cos }^3\left(x\right) dx$

Evaluate the indefinite integral: $\int 9x^2(a^2-x^2)dx$