Integrated x5 4 3 sec2 x sinh x dxSolutionsinhxex ex 2 al

Integrated; (x5 - 4 / 3 +sec2 (x) - sinh (x)- dx

Solution

sinh(x)=(e^x -e^-x )/2

all the terms can be integrated seperately

integrl (sec²x)= tanx+C1

integral (sinhx)=(1/2)(e^x +e^-x) +C2

integral(4/x³) =-2/x² +C3

so the final solution is:

x⁶/6+2/x² +tanx-(1/2)(e^x+e^-x) -7*x +C