What is the integral from 1 to sqrt(3 of)x3^{(x^2)} ?

The integral from 1 to sqrt(3 of)x3^{(x^2)} is (12)/(ln(3))

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integral from 1 to sqrt(3 of)x3^{(x^2)}

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

\frac{12}{ln ( 3 )}

Decimal

10.92287 \dots

Solution steps

\int_{1}^{3} x \cdot 3^{x^{2}} d x

Apply u-substitution

: \int_{3}^{27} \frac{1}{2 ln ( 3 )} d u

= \int_{3}^{27} \frac{1}{2 ln ( 3 )} d u

Integral of a constant:

\int a d x = a x

= [\frac{1}{2 ln ( 3 )} u]_{3}^{27}

Compute the boundaries:

\frac{12}{ln ( 3 )}

= \frac{12}{ln ( 3 )}

\frac{d y}{d x} = (\frac{2 y + 5}{4 x + 9})^{2}

\int_{0}^{\infty} \int_{0}^{\infty} e^{- x - y} d x d y

y = x^{3} - 5 x, y = 11 x

x \to 8 lim (\frac{\frac{8}{x} - 1}{x - 8})

\frac{d}{d x} (x^{\frac{4}{5}} (x - 9)^{2})

What is the integral from 1 to sqrt(3 of)x3^{(x^2)} ?
The integral from 1 to sqrt(3 of)x3^{(x^2)} is (12)/(ln(3))