What is the integral of (e^x)/2+xsqrt(x) ?

The integral of (e^x)/2+xsqrt(x) is 1/2 e^x+2/5 x^{5/2}+C

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integral of (e^x)/2+xsqrt(x)

\int \frac{e ^{x}}{2} + x x d x

\frac{1}{2} e^{x} + \frac{2}{5} x^{\frac{5}{2}} + C

Solution steps

\int \frac{e ^{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 \frac{e ^{x}}{2} d x + \int x x d x

\int \frac{e ^{x}}{2} d x = \frac{1}{2} e^{x}

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

= \frac{1}{2} e^{x} + \frac{2}{5} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{1}{2} e^{x} + \frac{2}{5} x^{\frac{5}{2}} + C

f (x) = - 3 cos (x), at x = - \frac{π}{3}

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

\frac{d}{d x} (3 x^{2} - y^{2})

\int sec (t) sec (t) + tan (t) d t

\int_{0}^{\infty} e^{- ∣ x ∣} d x

What is the integral of (e^x)/2+xsqrt(x) ?
The integral of (e^x)/2+xsqrt(x) is 1/2 e^x+2/5 x^{5/2}+C