7. Antiderivatives & Indefinite Integrals

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

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

Evaluate the indefinite integral. (Remember the constant of integration.) $\int ln\left(x\right) dx$

Evaluate the indefinite integral: $\int cos\left(6t\right) dt$

Evaluate the integral. (Use c for the constant of integration.) $\int wln\left(w\right)dw$

7-56. Trigonometric substitutions Evaluate the following integrals using trigonometric substitution.

16. ∫ x²/(25 + x²)² dx

Indefinite integrals Use a change of variables or Table 5.6 to evaluate the following indefinite integrals. Check your work by differentiating.                                                                                  

 ∫ [(√𝓍 + 1)⁴ / 2√𝓍 d𝓍

7–64. Integration review Evaluate the following integrals.

10. ∫ e^(3 - 4x) dx

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

Evaluate the indefinite integral: ${4x}^2+5x+1 dx$

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

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

Evaluate the indefinite integral as a power series: $\int \frac{1}{1-t^9} dt$.

Evaluate the indefinite integral. (Use c for the constant of integration.)

$${\int }_{}^{}\frac{sin\left(t\right)}{1+cos\left(t\right)} dt$$

Evaluate the definite integral if it exists: ${\int }_1^3{x}^2+2x+4 dx$