Page:Calculus Made Easy.pdf/171

 (3) $$y = \epsilon^{\frac{2x}{x+1}}$$.

Check by writing $$\dfrac{2x}{x+1}=z$$.

(4) $$y=\epsilon^{\sqrt{x^2+a}}$$. $$\log_\epsilon y=(x^2+a)^{\frac{1}{2}}$$.

(For if $$(x^2+a)^{\frac{1}{2}}=u$$ and $$x^2+a=v$$, $$u=v^{\frac{1}{2}}$$,

Check by writing $$\sqrt{x^2+a}=z$$.

(5) $$y=\log(a+x^3)$$. Let $$(a+x^3)=z$$; then $$y=\log_\epsilon z$$.

(6) $$y=\log_\epsilon\{{3x^2+\sqrt{a+x^2}}\}$$. Let $$3x^2 + \sqrt{a+x^2}=z$$; then $$y=\log_\epsilon z$$.