7. Antiderivatives & Indefinite Integrals

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

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

 ∫ (𝓍⁶ ― 3𝓍²)⁴ (𝓍⁵ ― 𝓍) d𝓍

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

Find $f\(\left\)(x\(\right\))$ by evaluating the following indefinite integral.

$f\left(x\right)=\int (8x^7+10x-20)dx$

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

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

125. ∫ dx / (√x * √(1 + x))

Finding Indefinite Integrals

Find the indefinite integrals (most general antiderivatives) in Exercises 73–88. You may need to try a solution and then adjust your guess. Check your answers by differentiation.

∫ 1/( r + 5)²dr

Find $f\(\left\)(x\(\right\))$ by evaluating the following indefinite integral.

$f\(\left\)(x\(\right\))=\(\int\[\left\)(100x^2-35x-\(\frac{13}{2}\]\right\))dx$

Finding Indefinite Integrals

In Exercises 17–56, find the most general antiderivative or indefinite integral. You may need to try a solution and then adjust your guess. Check your answers by differentiation.

∫(x + 1) dx

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

 ∫ 𝓍eˣ² d𝓍

Finding Indefinite Integrals

In Exercises 17–56, find the most general antiderivative or indefinite integral. You may need to try a solution and then adjust your guess. Check your answers by differentiation.

∫7sin(θ/3) dθ

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

∫ √(2x − x²) dx