What is the integral from 0 to 1 of x*3^{x^2+1} ?

The integral from 0 to 1 of x*3^{x^2+1} is 3/(ln(3))

Popular >

integral from 0 to 1 of x*3^{x^2+1}

\int_{0}^{1} x \cdot 3^{x^{2} + 1} d x

\frac{3}{ln ( 3 )}

Decimal Notation

2.73071 \dots

Solution steps

\int_{0}^{1} x \cdot 3^{x^{2} + 1} d x

Apply u-substitution

: \int_{1}^{2} \frac{3 ^{u}}{2} d u

= \int_{1}^{2} \frac{3 ^{u}}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{1}^{2} 3^{u} d u

\int a^{x} d x = \frac{a ^{x}}{ln a}

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

Compute the boundaries:

\frac{6}{ln ( 3 )}

= \frac{1}{2} \cdot \frac{6}{ln ( 3 )}

Simplify

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

y^{^{''}} + 9 y^{^{'}} + 18 y = 0, y (0) = 1, y^{^{'}} (0) = 0

\frac{\partial}{\partial x} (x^{3} + x e^{y} - 2 y)

\frac{d}{d x} (\frac{1}{( x + 2 ) ^{2}})

\int \frac{x ^{2}}{( x + 1 )} d x

What is the integral from 0 to 1 of x*3^{x^2+1} ?
The integral from 0 to 1 of x*3^{x^2+1} is 3/(ln(3))