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Popular >

integral of 1/y+x

Solution

\int \frac{1}{y} + x d x

Solution

\frac{x}{y} + \frac{x ^{2}}{2} + C

Solution steps

\int \frac{1}{y} + 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{1}{y} d x + \int x d x

\int \frac{1}{y} d x = \frac{x}{y}

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

= \frac{x}{y} + \frac{x ^{2}}{2}

Add a constant to the solution

= \frac{x}{y} + \frac{x ^{2}}{2} + C

Popular Examples

integral of 2sqrt((4-t^2)/(t^8))

\int 2 \frac{4 - t ^{2}}{t ^{8}} d t

integral of (e^x+2x+3)

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

integral of (3x^2)/(x^3-4)

\int \frac{3 x ^{2}}{x ^{3} - 4} d x

integral of (5a)/(sqrt(x))

\int \frac{5 a}{x} d x

integral of 81e^{9x}sin(9x)

\int 81 e^{9 x} sin (9 x) d x

Frequently Asked Questions (FAQ)

What is the integral of 1/y+x ?
The integral of 1/y+x is x/y+(x^2)/2+C