Find the integral

Question

Answer 1

Question 6:

∫ x^3/4 + 7x^-5 + ¹/₆ x^-1/2 dx

= ⁴/₇ x^7/4 - ⁷/₄ x^-4 + ¹/₃ x^1/2 + C

Question 7:

∫ (w + w^1/3)(4 - w²) dw

= ∫ 4w - w³ + 4w^1/3 - w^7/3 dw

= 2w² - ¹/₄ w⁴ + 3w^4/3 - ³/₁₀w^10/3 + C

Answer 2

6) Integrals can be broken up into the sum of separate integrals. You can write all of these integrals as powers of x and use the power rule int(xⁿ) = xⁿ⁺¹/n+1 for all real n except -1:

int( ( 2x^3/4 + 7x^-5 + 1/6 (x^-1/2))dx

7) Multiply the integral out and integrate each term: int( 4w-w³ + 4w^1/3 - w^7/3)dw