What is the integral of 5xsqrt(1^2+5^2) ?

The integral of 5xsqrt(1^2+5^2) is (5sqrt(13)x^2)/(sqrt(2))+C

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integral of 5xsqrt(1^2+5^2)

\int 5 x 1^{2} + 5^{2} d x

\frac{5 13 x ^{2}}{2} + C

Solution steps

\int 5 x 1^{2} + 5^{2} d x

Take the constant out:

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

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

Simplify

= 526 \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= 526 \frac{x ^{2}}{2}

Simplify

526 \frac{x ^{2}}{2} : \frac{5 13 x ^{2}}{2}

= \frac{5 13 x ^{2}}{2}

Add a constant to the solution

= \frac{5 13 x ^{2}}{2} + C

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What is the integral of 5xsqrt(1^2+5^2) ?
The integral of 5xsqrt(1^2+5^2) is (5sqrt(13)x^2)/(sqrt(2))+C