1.
Find the following integrals:
(a)
\(\ds \int x(x^2+4)^2 dx\)
(b)
\(\ds \int \dfrac{1}{e^{2x}} dx\)
(c)
\(\ds \int \cos^3(2x)\sin(2x) dx\)
(d)
\(\ds \int 2x\sin(x^2) dx\)
(e)
\(\ds \int e^{\sin x}\cos x dx\)
(f)
\(\ds \int \frac{\sin \sqrt{x}}{\sqrt{x}} dx\)
(g)
\(\ds \int \frac{e^{\sqrt[3]{x}}}{\sqrt[3]{x^2}} dx\)
(h)
\(\ds \int \frac{dx}{x\ln(2x)}\)
(i)
\(\ds \int \frac{\cos x}{2\sin(x) +3} dx\)
(j)
\(\ds \int \frac{x^3}{x^4+1} dx\)
(k)
\(\ds \int x\sec(2x^2 -3) dx.\)
(l)
\(\ds \int \frac{\sin\left( \frac{1}{x} \right)}{x^2} dx\)
(m)
\(\ds \int \frac{2x-1}{\left( 2x^2 -2x+1 \right)^3} dx\)
(n)
\(\ds \int 3e^{3x}\sin(e^{3x}) dx\)
(o)
\(\ds \int x^2\sqrt{1+x^3} dx\)
