What is the integral from 2 to 3 of (xe^{3x}-2ln(x)) ?

The integral from 2 to 3 of (xe^{3x}-2ln(x)) is (8e^9-5e^6)/9-2(3ln(3)-1-2ln(2))

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integral from 2 to 3 of (xe^{3x}-2ln(x))

\int_{2}^{3} (x e^{3 x} - 2 ln (x)) d x

\frac{8 e ^{9} - 5 e ^{6}}{9} - 2 (3 ln (3) - 1 - 2 ln (2))

Decimal

6976.79507 \dots

Solution steps

\int_{2}^{3} x e^{3 x} - 2 ln (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{2}^{3} x e^{3 x} d x - \int_{2}^{3} 2 ln (x) d x

\int_{2}^{3} x e^{3 x} d x = \frac{8 e ^{9} - 5 e ^{6}}{9}

\int_{2}^{3} 2 ln (x) d x = 2 (3 ln (3) - 1 - 2 ln (2))

= \frac{8 e ^{9} - 5 e ^{6}}{9} - 2 (3 ln (3) - 1 - 2 ln (2))

\int_{0}^{x} tan (x) d x

\int_{- 1}^{0} (2 x + e^{x}) d x

\int_{0}^{1} x e^{- 1} d x

\int_{1}^{4} (x^{4} + 5 x^{2}) d x

\int_{0}^{2} x^{3} (2 + x^{4})^{3} d x

What is the integral from 2 to 3 of (xe^{3x}-2ln(x)) ?
The integral from 2 to 3 of (xe^{3x}-2ln(x)) is (8e^9-5e^6)/9-2(3ln(3)-1-2ln(2))