Apply appropriate transformations to compute the integrals a x 2 2 3 x 2 2 dx b

# Apply appropriate transformations to compute the

• Notes
• 67
• 100% (1) 1 out of 1 people found this document helpful

This preview shows page 49 - 52 out of 67 pages.

Problem 5.Apply appropriate transformations tocompute the integrals (a)x2(23x2)2dx;(b)x(1x)10dx;(c)1+x1x;(d)x21+xdx;(e)x33+xdx;(f)(1+x)21+x2dx;(g)(2x)22x2dx;(h)x2dx(1x)100;(i)x5dxx+1;(j)dxx+1+x1;(k)x25xdx;(l)dx(x1)(x+3);(m)dxx2+x2;(n)dx(x2+1)(x2+2);(o)dx(x22)(x2+3);(p)dx(x+2)(x+3);(q)dxx4+3x2+2;(r)dx(x+a)2(x+b)2, wherea̸=b;(s)dx(x2+a2)(x2+b2), wherea2̸=b2.Problem 6.Apply appropriate transformations tocompute the integrals(a)sin2xdx;(b)cos2xdx;(c)sinxsin(x+α)dx;(d)sin 3xsin 5xdx;(e)cosx2cosx3dx;(f)sin(2xπ6)cos(3x+π4)dx;(g)sin3xdx;(h)cos3xdx;(i)sin4xdx;(j)cos4xdx;(k)cot2xdx;(l)tan2xdx;(m)sin23xsin32xdx;(n)dxsin2xcos2x;(o)dxsin2xcosx;(p)dxsinxcos3x;(q)cos3xsinxdx;49
(r)dxcos4x;(s)dx1+ex;(t)(1+ex)21+e2xdx;(u)sinh2xdx;(v)cosh2xdx;(w)sinhxsinh 2xdx;(x)coshxcosh 3xdx;(y)dxsinh2xcosh2x.Problem 7.Use the substitution rule to computethe following integrals(a)x231xdx;(b)x3(15x2)10dx;(c)x22x;(d)x51x2dx;(e)x5(25x3)2/3dx;(f)cos5xsinxdx;(g)sinxcos3x1+cos2xdx;(h)sin2xcos6xdx;(i)dxx1+lnx;(j)dxex/2+ex;(k)dx1+ex;(l)arctanxx·dx1+x.Problem 8.Use trigonometric substitutions tofind the following integrals Problem 9.Use hyperbolic substitutions to findthe following integrals Problem 10.Apply the integration by parts ruleto compute the following integrals )2dx;(j)x3cosh 3xdx;(k)arctanxdx;(l)arcsinxdx;(m)xarctanxdx;(n)x2arccosxdx;(o)arcsinxx2dx ; 50
(p)ln(x+1 +x2)dx;(q)xln1+x1xdx;(r)arctanxdx;(s)sinxln(tanx)dx;