7. Antiderivatives & Indefinite Integrals

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

Evaluate the indefinite integral: ${\int }_{}^{}5x^2+25 dx$

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

71. Different Methods

Let I = ∫ (x²)/(x + 1) dx.

b. Evaluate I by first performing long division on the integrand.

Evaluate the indefinite integral. Remember to include the constant of integration.
$${\int }_{}^{}{(\ln (x\left)\right)}^{2}dx$$

Evaluate the integral. (Use c for the constant of integration.) $\int \ln \left(x\right) dx$

Evaluate the indefinite integral: ${\int }_{}^{}\frac{5}{1+x^2}dx$

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

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

Evaluate the integral. (Use $c$ for the constant of integration.) $\int x{x}^4+16dx$

Using an upper-case C for any arbitrary constants, find the general indefinite integral: ${\int }_{}^{}{x}^{2}dx$ =

Evaluate the indefinite integral: $0.75x^2-16x^2 dx$

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

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: $\int (2x^2+3x+1)dx$