What is the integral of (5x^2+1)e^{(5/3 x^3+x)} ?

The integral of (5x^2+1)e^{(5/3 x^3+x)} is e^{5/3 x^3+x}+C

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integral of (5x^2+1)e^{(5/3 x^3+x)}

\int (5 x^{2} + 1) e^{(\frac{5}{3} x^{3} + x)} d x

e^{\frac{5}{3} x^{3} + x} + C

Solution steps

\int (5 x^{2} + 1) e^{\frac{5}{3} x^{3} + x} d x

Apply u-substitution

: \int e^{u} d u

= \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= e^{u}

Substitute back

u = \frac{5}{3} x^{3} + x

= e^{\frac{5}{3} x^{3} + x}

Add a constant to the solution

= e^{\frac{5}{3} x^{3} + x} + C

\int 5 x^{2} - 4 d x

\frac{d ^{2}}{d x ^{2}} (e^{\frac{- x ^{2}}{2}})

y = 7 x - 6 x, (1, 1)

y^{^{''}} + 9 y^{^{'}} - 10 y = 0

\frac{d y}{d x} = 2 + y - 2 x + 3

What is the integral of (5x^2+1)e^{(5/3 x^3+x)} ?
The integral of (5x^2+1)e^{(5/3 x^3+x)} is e^{5/3 x^3+x}+C