Evaluate : i. ∫(x^2 - 1/x^2)^3 ii. ∫(√x - 1/√x)dx iii. ∫(√x + 1/√x)^2dx iv. ∫(1 + 2x)/x^4dx v. ∫(1 + x)√x dx

Question

Evaluate :

i. \(\int(x^2-\frac{1}{x^2})^{3}dx\)

∫(x² - 1/x²)³

ii. \(\int(\sqrt{x}-\frac{1}{\sqrt{x}})dx\)

∫(√x - 1/√x)dx

iii. \(\int(\sqrt{x}+\frac{1}{\sqrt{x}})^2 dx\)

∫(√x + 1/√x)²dx

iv. \(\int \frac{(1\,+\,2x)}{x^4}dx\)

∫(1 + 2x)/x⁴dx

v. \(\int\frac{(1\,+\,x)}{\sqrt{x}}dx\)

∫(1 + x)√x dx

vi. \(\int\frac{2x^2\,+\,x\,-\,2}{(x-2)}dx\)

∫2x² + x - 2/(x - 2)dx

Answer 1

i. Given:

= ∫x⁶ +x^-6 -3x²-3x^-2 dx

ii. Given:

iii. Given:

iv. Given:

v. Given:

vi. Given:

=x²- 4x+8x+8 ln|x-2|+x + c

=x² +5x+8 ln|x-2|+c