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81.

$ \int x \ln x dx = x^2 \left[\dfrac{\ln x}{2}-\dfrac{1}{4}\right] + C $

82.

$ \int x^n \ln x dx = x^{n+1} \left[\dfrac{\ln x}{n+1}-\dfrac{1}{(n+1)^2}\right] + C $

83.

$\int e^{ax} \sin bx dx = \dfrac{a\sin bx - b \cos bx}{a^2+b^2} e^{ax} + C $

84.

$\int e^{ax} \cos bx dx = \dfrac{a\cos bx - b \sin bx}{a^2+b^2} e^{ax} + C $

85.

$ \int \sinh x dx = \cosh x + C$

86.

$ \int \cosh x dx = \sinh x + C $

87.

$ \tanh x dx = \ln \cosh x + C$

88.

$ \int \coth x dx = \ln|\sinh x| + C $

89.

$ \int \text{sech}^2 x dx = \tanh x + C $

90.

$ $ \int \text{csch}^2 x dx = -\coth x + C $ $

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