What is the integral of 7sqrt(x^2)+xsqrt(x) ?

The integral of 7sqrt(x^2)+xsqrt(x) is (7x^2)/2+2/5 x^{5/2}+C

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integral of 7sqrt(x^2)+xsqrt(x)

\int 7 x^{2} + x x d x

\frac{7 x ^{2}}{2} + \frac{2}{5} x^{\frac{5}{2}} + C

Solution steps

\int 7 x^{2} + x x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 7 x^{2} d x + \int x x d x

\int 7 x^{2} d x = \frac{7 x ^{2}}{2}

\int x x d x = \frac{2}{5} x^{\frac{5}{2}}

= \frac{7 x ^{2}}{2} + \frac{2}{5} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{7 x ^{2}}{2} + \frac{2}{5} x^{\frac{5}{2}} + C

\frac{d y}{d t} = 6 y + cos (3 t), y (0) = \frac{28}{15}

\int 7 5 (8 - 2 x)^{8} d x

f (x) = x^{4} + 6 x^{2} - x, at x = 1

\frac{d}{d x} (ln (\frac{a}{x}))

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

What is the integral of 7sqrt(x^2)+xsqrt(x) ?
The integral of 7sqrt(x^2)+xsqrt(x) is (7x^2)/2+2/5 x^{5/2}+C