91Ó°ÊÓ

Calculate each of the indefinite integrals. $$ \int \frac{3 x^{3}-16 x^{2}+26 x-14}{(x-1)^{2}(x-2)^{2}} d x $$

Let \(b\) be the abscissa of the point of intersection of the graphs of \(y=x^{4}+2\) and \(y=\frac{5 x^{3}+3 x+2}{x^{3}+x^{2}+x+1}\) for \(0

An income stream \(f(t)\) is given (in dollars per year with \(t=0\) corresponding to the present). The income will commence \(T_{1}\) years in the future and continue in perpetuity. Calculate the present value of the income stream assuming that the discount rate is \(5 \%\). $$ f(t)=1000+50 t ; T_{1}=0 $$

Evaluate the given integral by converting the integrand to an expression in sines and cosines. $$ \int 3 \tan (x) \sec ^{3}(x) d x $$

Calculate the given integral by first integrating by parts and then making a trigonometric substitution. $$ \int_{\sqrt{2}}^{2} \operatorname{arcsec}(x) d x $$

An income stream \(f(t)\) is given (in dollars per year with \(t=0\) corresponding to the present). The income will commence \(T_{1}\) years in the future and continue in perpetuity. Calculate the present value of the income stream assuming that the discount rate is \(5 \%\). $$ f(t)=1000+50 t ; T_{1}=20 $$

Evaluate the given integral by converting the integrand to an expression in sines and cosines. $$ \int \tan ^{3}(x / 2) d x $$

Evaluate each of the integrals. $$ \int 9 \sqrt{x} \ln (x) d x $$

Calculate the given integral by first integrating by parts and then making a trigonometric substitution. $$ \int_{0}^{1 / \sqrt{2}} x \arcsin (x) d x $$

Calculate each of the indefinite integrals. $$ \int \frac{5 x^{3}+5 x^{2}-x-2}{\left(x^{2}+x\right)^{2}} d x $$