1 / | | 1 | ------------------- dx | 2 2 | cosh (x) + sinh (x) | / 0
Integral(1/(cosh(x)^2 + sinh(x)^2), (x, 0, 1))
/ /x\ \ / /x\ \ / /x\ \ / /x\ \ | tanh|-| | | tanh|-| | _____________ _____________ | tanh|-| | _____________ _____________ | tanh|-| | | \2/ | ___ | \2/ | / ___ / ___ | \2/ | ___ / ___ / ___ | \2/ | 3*atan|----------------| 2*\/ 2 *atan|----------------| 3*\/ 3 - 2*\/ 2 *\/ 3 + 2*\/ 2 *atan|----------------| 2*\/ 2 *\/ 3 - 2*\/ 2 *\/ 3 + 2*\/ 2 *atan|----------------| / | _____________| | _____________| | _____________| | _____________| | | / ___ | | / ___ | | / ___ | | / ___ | | 1 \\/ 3 - 2*\/ 2 / \\/ 3 - 2*\/ 2 / \\/ 3 + 2*\/ 2 / \\/ 3 + 2*\/ 2 / | ------------------- dx = C + --------------------------------------------- + --------------------------------------------- - ---------------------------------------------------------- - ---------------------------------------------------------------- | 2 2 _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ | cosh (x) + sinh (x) / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ | 7*\/ 3 - 2*\/ 2 + 5*\/ 2 *\/ 3 - 2*\/ 2 7*\/ 3 - 2*\/ 2 + 5*\/ 2 *\/ 3 - 2*\/ 2 7*\/ 3 - 2*\/ 2 + 5*\/ 2 *\/ 3 - 2*\/ 2 7*\/ 3 - 2*\/ 2 + 5*\/ 2 *\/ 3 - 2*\/ 2 /
_____________ _____________ _____________ _____________ / tanh(1/2) \ ___ / tanh(1/2) \ / ___ / ___ / tanh(1/2) \ ___ / ___ / ___ / tanh(1/2) \ 3*atan|----------------| 2*\/ 2 *atan|----------------| 3*\/ 3 - 2*\/ 2 *\/ 3 + 2*\/ 2 *atan|----------------| 2*\/ 2 *\/ 3 - 2*\/ 2 *\/ 3 + 2*\/ 2 *atan|----------------| | _____________| | _____________| | _____________| | _____________| | / ___ | | / ___ | | / ___ | | / ___ | \\/ 3 - 2*\/ 2 / \\/ 3 - 2*\/ 2 / \\/ 3 + 2*\/ 2 / \\/ 3 + 2*\/ 2 / --------------------------------------------- + --------------------------------------------- - ---------------------------------------------------------- - ---------------------------------------------------------------- _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ 7*\/ 3 - 2*\/ 2 + 5*\/ 2 *\/ 3 - 2*\/ 2 7*\/ 3 - 2*\/ 2 + 5*\/ 2 *\/ 3 - 2*\/ 2 7*\/ 3 - 2*\/ 2 + 5*\/ 2 *\/ 3 - 2*\/ 2 7*\/ 3 - 2*\/ 2 + 5*\/ 2 *\/ 3 - 2*\/ 2
=
_____________ _____________ _____________ _____________ / tanh(1/2) \ ___ / tanh(1/2) \ / ___ / ___ / tanh(1/2) \ ___ / ___ / ___ / tanh(1/2) \ 3*atan|----------------| 2*\/ 2 *atan|----------------| 3*\/ 3 - 2*\/ 2 *\/ 3 + 2*\/ 2 *atan|----------------| 2*\/ 2 *\/ 3 - 2*\/ 2 *\/ 3 + 2*\/ 2 *atan|----------------| | _____________| | _____________| | _____________| | _____________| | / ___ | | / ___ | | / ___ | | / ___ | \\/ 3 - 2*\/ 2 / \\/ 3 - 2*\/ 2 / \\/ 3 + 2*\/ 2 / \\/ 3 + 2*\/ 2 / --------------------------------------------- + --------------------------------------------- - ---------------------------------------------------------- - ---------------------------------------------------------------- _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ 7*\/ 3 - 2*\/ 2 + 5*\/ 2 *\/ 3 - 2*\/ 2 7*\/ 3 - 2*\/ 2 + 5*\/ 2 *\/ 3 - 2*\/ 2 7*\/ 3 - 2*\/ 2 + 5*\/ 2 *\/ 3 - 2*\/ 2 7*\/ 3 - 2*\/ 2 + 5*\/ 2 *\/ 3 - 2*\/ 2
3*atan(tanh(1/2)/sqrt(3 - 2*sqrt(2)))/(7*sqrt(3 - 2*sqrt(2)) + 5*sqrt(2)*sqrt(3 - 2*sqrt(2))) + 2*sqrt(2)*atan(tanh(1/2)/sqrt(3 - 2*sqrt(2)))/(7*sqrt(3 - 2*sqrt(2)) + 5*sqrt(2)*sqrt(3 - 2*sqrt(2))) - 3*sqrt(3 - 2*sqrt(2))*sqrt(3 + 2*sqrt(2))*atan(tanh(1/2)/sqrt(3 + 2*sqrt(2)))/(7*sqrt(3 - 2*sqrt(2)) + 5*sqrt(2)*sqrt(3 - 2*sqrt(2))) - 2*sqrt(2)*sqrt(3 - 2*sqrt(2))*sqrt(3 + 2*sqrt(2))*atan(tanh(1/2)/sqrt(3 + 2*sqrt(2)))/(7*sqrt(3 - 2*sqrt(2)) + 5*sqrt(2)*sqrt(3 - 2*sqrt(2)))
Use the examples entering the upper and lower limits of integration.