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

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

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

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: $\int 9x^2(a^2-x^2)dx$

Evaluate the indefinite integral as a power series: $\int \frac{1}{1-t^7} dt$.

23–68. Indefinite integrals Determine the following indefinite integrals. Check your work by differentiation.

∫ (3x⁵ - 5x⁹) dx