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Popular >

integral of x+(3y)/x

Solution

\int x + \frac{3 y}{x} d x

Solution

3 y ln ∣ x ∣ + \frac{x ^{2}}{2} + C

Solution steps

\int x + \frac{3 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{3 y}{x} d x + \int x d x

\int \frac{3 y}{x} d x = 3 y ln ∣ x ∣

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

= 3 y ln ∣ x ∣ + \frac{x ^{2}}{2}

Add a constant to the solution

= 3 y ln ∣ x ∣ + \frac{x ^{2}}{2} + C

Popular Examples

integral of 16cos^4(5pi)t

\int 16 cos^{4} (5 π) t d t

integral of (4x)/(sqrt(11+10x-x^2))

\int \frac{4 x}{11 + 10 x - x ^{2}} d x

integral of x/(3x+5)

\int \frac{x}{3 x + 5} d x

integral of x^3(x+7)^9

\int x^{3} (x + 7)^{9} d x

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

\int \frac{( 2 + x ) ^{2}}{x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral of x+(3y)/x ?
The integral of x+(3y)/x is 3yln|x|+(x^2)/2+C