What is the integral from 1 to 4 of 2xsqrt(5+x^2) ?

The integral from 1 to 4 of 2xsqrt(5+x^2) is 2(7sqrt(21)-2sqrt(6))

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integral from 1 to 4 of 2xsqrt(5+x^2)

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

2 (721 - 26)

Decimal Notation

54.35810 \dots

Solution steps

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

Take the constant out:

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

= 2 \cdot \int_{1}^{4} x 5 + x^{2} d x

Apply u-substitution

: \int_{6}^{21} u^{2} d u

= 2 \cdot \int_{6}^{21} u^{2} d u

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{6}^{21}

= 2 [\frac{u ^{3}}{3}]_{6}^{21}

Compute the boundaries:

721 - 26

= 2 (721 - 26)

\frac{\partial}{\partial x} (e^{a x^{3}})

y = sec (5 x)

\int \frac{1}{sin ( θ ) ( cos ^{2} ( θ ) + 4 )} d x

\int e^{1.5 x} d x

\int e^{6 x} sin (4 x) d x

What is the integral from 1 to 4 of 2xsqrt(5+x^2) ?
The integral from 1 to 4 of 2xsqrt(5+x^2) is 2(7sqrt(21)-2sqrt(6))