7. Antiderivatives & Indefinite Integrals

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

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

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

∫ (3x⁵ - 5x⁹) dx

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

∫ (4√x - (4 /√x)) dx

Evaluating integrals Evaluate the following integrals.                                                                                                                                         

 ∫ (9𝓍⁸―7𝓍⁶) d𝓍

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

∫ (5s + 3)² ds

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

∫ (3x ¹⸍³ + 4x ⁻¹⸍³ + 6) dx

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

∫ (3x + 1) (4 - x) dx

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

∫ (3/x⁴ + 2 - 3/x²)

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

∫ ((4x⁴ - 6x²) / x ) dx

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

∫ (x² - 36) / (x - 6) dx

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

∫ (csc² Θ + 2Θ² - 3Θ) dΘ

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

∫ ((2 + 3 cos y)/sin² y)dy

Evaluating integrals Evaluate the following integrals.                                                                                                                                         

 ∫ y² /(y³ + 27) dy

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

∫ (sec² x - 1) dx

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

∫ (sec² Θ + sec Θ tan Θ)dΘ