What is the integral of (100)/(25+(5y)^2)+e^4 ?

The integral of (100)/(25+(5y)^2)+e^4 is 4arctan(y)+e^4y+C

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integral of (100)/(25+(5y)^2)+e^4

\int \frac{100}{25 + ( 5 y ) ^{2}} + e^{4} d y

4 arctan (y) + e^{4} y + C

Solution steps

\int \frac{100}{25 + ( 5 y ) ^{2}} + e^{4} 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 \frac{100}{25 + ( 5 y ) ^{2}} d y + \int e^{4} d y

\int \frac{100}{25 + ( 5 y ) ^{2}} d y = 4 arctan (y)

\int e^{4} d y = e^{4} y

= 4 arctan (y) + e^{4} y

Add a constant to the solution

= 4 arctan (y) + e^{4} y + C

\frac{y ( 4 x + 4 y )}{( x ^{2} + y ^{2} )}

\int_{1}^{4} x^{2} + 2 d x

\frac{\partial}{\partial x} (2 x^{3 y})

\frac{\partial}{\partial t} (- 3 s t)

(0.1666) (0.998)^{x}

What is the integral of (100)/(25+(5y)^2)+e^4 ?
The integral of (100)/(25+(5y)^2)+e^4 is 4arctan(y)+e^4y+C