Printed Page 523
523
Skill Building
In Problems 1–16, find each integral using the Table of Integrals found at the back of the book.
∫e2xcosxdx
15e2x(2cosx+sinx)+C
∫e5x+1sin(2x+3)dx
∫x√4x+3dx
120(2x−1)(3+4x)3/2+C
∫dx(x2−1)3/2
∫(x+1)√4x+5dx
6x+560(4x+5)3/2+C
∫dx[(2x+3)2−1]3/2
∫dxx√4x+6
√66ln|√6+4x−√6√6+4x+√6|+C
∫dxx√8+x
∫√4x+6xdx
2√6+4x+√6ln|√6+4x−√6√6+4x+√6|+C
∫√8+xx2dx
∫x3(lnx)2dx
x4(lnx)24−x4lnx8+x432+C
∫x3(lnx)2dx
∫sin−1(2x)dx
xsin−1(2x)+12√1−4x2+C
∫tan−1(−3x)dx
∫21x3√3x−x2dx
1358sin−113−9√24
∫e11x2√x2+2dx
In Problems 17–32:
∫e2xcosxdx
∫x√4x+3dx
∫(x+1)√4x+5dx
∫dxx√4x+6
∫√4x+6xdx
∫x3(lnx)2dx
∫sin−1(2x)dx
∫21x3√3x−x2dx
In Problems 33–38, use a CAS to investigate whether each indefinite integral can be expressed using elementary functions.
∫√1+x3dx
No
∫√1+sinxdx
∫e−x2dx
No
∫cosxxdx
∫xtanxdx
No
∫√1+exdx