CALCULUS 2 GATEWAY EXAM WITH CORRECT ANSWERS -4.

CALCULUS 2 GATEWAY EXAM WITH CORRECT
ANSWERS #4
= u +c - correct answer ∫ du

= [uⁿ⁺¹] / (n+1) +c - correct answer ∫ uⁿ du

= ln|u| +c - correct answer ∫ du/u

= eⁿ +c - correct answer ∫ eⁿ dn

= (aⁿ)/ln|a| +c - correct answer ∫ aⁿ dn

= -cos u +c - correct answer ∫ sin u du

= sin u +c - correct answer ∫ cos u du

= tan u +c - correct answer ∫ sec² u du

= -cot u +c - correct answer ∫ csc² u du

= sec u +c - correct answer ∫ sec u tan u du

= -csc u +c - correct answer ∫ csc u cot u du

= ln|sec u| +c - correct answer ∫ tan u du

= ln|sin u| +c - correct answer ∫ cot u du

= ln|sec u + tan u| +c - correct answer ∫ sec u du

= ln|csc u - cot u| +c - correct answer ∫ csc u du

= sin²(u/a) +c, a > 0 - correct answer ∫ du / √(a² - u²)

= (¹/a)tan⁻¹(u/a) +c - correct answer ∫ du / (a² + u²)

= (¹/a)sec⁻¹(u/a) +c - correct answer ∫ du / [u √(u² - a²)]

= (¹/2a) ln|(u+a)/(u-a)| +c - correct answer ∫ du / (a² - u²)

= (¹/2a) ln|(u-a)/(u+a)| +c - correct answer ∫ du / (u² - a²)

A/x + B/(x-2) + C/(x-2)² + (Dx+E)/(x²+5) + (Ex+F)/(x²+5)² - correct answer Partial
fractions decomposition form: