What is the integral of 7/(1+x^2) ?

The integral of 7/(1+x^2) is 7arctan(x)+C

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integral of 7/(1+x^2)

\int \frac{7}{1 + x ^{2}} d x

7 arctan (x) + C

Solution steps

\int \frac{7}{1 + x ^{2}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 7 \cdot \int \frac{1}{1 + x ^{2}} d x

Use the common integral:

\int \frac{1}{1 + x ^{2}} d x = arctan (x)

= 7 arctan (x)

Add a constant to the solution

= 7 arctan (x) + C

x \to 3 lim (x^{2} + 5)

\frac{( s - 5 )}{( s ^{2} + 4 s + 20 )}

y^{^{'}} + 8 y = 56

x \to - 2 + lim (\frac{1}{( x + 2 ) ^{2}})

\int_{0}^{\frac{π}{3}} tan (x) d x