What is the integral from 0 to 3 of xsqrt(1+4x^2) ?

The integral from 0 to 3 of xsqrt(1+4x^2) is (37sqrt(37)-1)/(12)

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integral from 0 to 3 of xsqrt(1+4x^2)

\int_{0}^{3} x 1 + 4 x^{2} d x

\frac{37 37 - 1}{12}

Solution steps

\int_{0}^{3} x 1 + 4 x^{2} d x

Apply u-substitution

: \int_{1}^{37} \frac{u}{8} d u

= \int_{1}^{37} \frac{u}{8} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int_{1}^{37} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{37}

= \frac{1}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{37}

Compute the boundaries:

\frac{74 37}{3} - \frac{2}{3}

= \frac{1}{8} (\frac{74 37}{3} - \frac{2}{3})

Simplify

= \frac{37 37 - 1}{12}

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

\int_{1}^{0} \frac{1}{x} d x

\int_{0}^{6} (x^{2} + 1) e^{3 x} d x

\int_{- 1}^{2} 4^{x} e^{2 x} d x

\int_{3}^{x} 9 x d x

What is the integral from 0 to 3 of xsqrt(1+4x^2) ?
The integral from 0 to 3 of xsqrt(1+4x^2) is (37sqrt(37)-1)/(12)