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Jonathan Manzanares

This document contains solutions to several calculus integral problems. It finds the antiderivatives of x/(1-x^2), x^2*x^i-1, and x^4/(x^5-3) by using u-substitution and obtaining 1/2(1-x^2), 2/9(x^i-1)^(3/2), and 2/5√(x^5-3) respectively.

Matemáticas
Calculo integral
Jonathan Gerardo Manzanares Castañeda

∫xdx/(1-x²)=
-½∫(1-x²)-²(-2)xdx
V=1-x²
DV=-2xdx ̸ = -½ (1-x²)/1+c
=½(1-x²)¯ⁱ4c

∫x² xⁱ-1dx
⅓∫(xⁱ-1)½ 3x²dx
V=xⁱ-1
DV=3x²dx /= ⅓ (xⁱ-1)ⁱ'² 3/2+c
=2/9=(xⁱ-1)ⁱ’²+c

∫x⁴dx/x⁵-3=
⅕∫(x⁵-3)¯⅟² 5x⁴dx=
⅕(x⁵-3) ⅟² +c =
2/5√x⁵-3+c

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Tarea de mate

1. Matemáticas Calculo integral Jonathan Gerardo Manzanares Castañeda

2. ∫xdx/(1-x²)= -½∫(1-x²)-²(-2)xdx V=1-x² DV=-2xdx ̸ = -½ (1-x²)/1+c =½(1-x²)¯ⁱ4c

3. ∫x² xⁱ-1dx ⅓∫(xⁱ-1)½ 3x²dx V=xⁱ-1 DV=3x²dx /= ⅓ (xⁱ-1)ⁱ'² 3/2+c =2/9=(xⁱ-1)ⁱ’²+c

4. ∫x⁴dx/x⁵-3= ⅕∫(x⁵-3)¯⅟² 5x⁴dx= ⅕(x⁵-3) ⅟² +c = 2/5√x⁵-3+c