7. Antiderivatives & Indefinite Integrals

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

Evaluate the indefinite integral. (Use c for the constant of integration.)
$${\int }_{}^{}{\cos }^{-1}\left(x\right) dx$$

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

Evaluate the indefinite integral: ${\int }_{}^{}(x^3-8x^2-7x+10)dx$

Evaluate the integral. (Use c for the constant of integration.) ${\int }_{}^{}{\sin }^{-1}\left(x\right)dx$

Evaluate the indefinite integral as a power series: $\int \arctan \left(x\right)x dx$

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.) $4x^5 \int dx$