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Popular >

integral of 3x^2y+e^y

Solution

\int 3 x^{2} y + e^{y} d x

Solution

e^{y} x + y x^{3} + C

Solution steps

\int 3 x^{2} y + e^{y} 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 e^{y} d x + \int 3 y x^{2} d x

\int e^{y} d x = e^{y} x

\int 3 y x^{2} d x = y x^{3}

= e^{y} x + y x^{3}

Add a constant to the solution

= e^{y} x + y x^{3} + C

Popular Examples

integral from 0 to pi/2 of xcos(x)

\int_{0}^{\frac{π}{2}} x cos (x) d x

(dx)/(dy)+2xy=4y

\frac{d x}{d y} + 2 x y = 4 y

integral of (arctan(x))/(x^3)

\int \frac{arctan ( x )}{x ^{3}} d x

integral of 14x^6y^{-4}-12x^{5y^{-3}}

\int 14 x^{6} y^{- 4} - 12 x^{5 y^{- 3}} d x

(\partial)/(\partial x)(cos(2x-y))

\frac{\partial}{\partial x} (cos (2 x - y))

Frequently Asked Questions (FAQ)

What is the integral of 3x^2y+e^y ?
The integral of 3x^2y+e^y is e^yx+yx^3+C