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Popular >

integral of 2+x+ye^y

Solution

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

Solution

2 y + x y + e^{y} y - e^{y} + C

Solution steps

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

Apply the Sum Rule:

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

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

\int 2 d y = 2 y

\int x d y = x y

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

= 2 y + x y + e^{y} y - e^{y}

Add a constant to the solution

= 2 y + x y + e^{y} y - e^{y} + C

Popular Examples

integral of (x^3+5)^{100}(3x^2)

\int (x^{3} + 5)^{100} (3 x^{2}) d x

integral of (ln(x))/((x^3*ln(x^3)))

\int \frac{ln ( x )}{( x ^{3} \cdot ln ( x ^{3} ) )} d x

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

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

integral of 9/(xln(6x))

\int \frac{9}{x ln ( 6 x )} d x

integral of 4/(3+2x)

\int \frac{4}{3 + 2 x} d x

Frequently Asked Questions (FAQ)

What is the integral of 2+x+ye^y ?
The integral of 2+x+ye^y is 2y+xy+e^yy-e^y+C