What is the integral of x^2y+tanh(x) ?

The integral of x^2y+tanh(x) is tanh(x)y+(x^2y^2)/2+C

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integral of x^2y+tanh(x)

\int x^{2} y + tanh (x) d y

tanh (x) y + \frac{x ^{2} y ^{2}}{2} + C

Solution steps

\int x^{2} y + tanh (x) 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 tanh (x) d y + \int x^{2} y d y

\int tanh (x) d y = tanh (x) y

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

= tanh (x) y + \frac{x ^{2} y ^{2}}{2}

Add a constant to the solution

= tanh (x) y + \frac{x ^{2} y ^{2}}{2} + C

x \to 1 lim (1 - 5)

x \to \infty lim (\frac{12}{x})

\frac{d}{d t} (4 t^{2})

(2 x y^{2} + 5 y) + (2 x^{2} y + 5 x) y^{^{'}} = 0

\int_{0}^{\frac{π}{2}} ln (sin (x)) d x

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