What is the integral of 7/(9+16x^2) ?

The integral of 7/(9+16x^2) is 7/12 arctan(4/3 x)+C

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integral of 7/(9+16x^2)

\int \frac{7}{9 + 16 x ^{2}} d x

\frac{7}{12} arctan (\frac{4}{3} x) + C

Solution steps

\int \frac{7}{9 + 16 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}{9 + 16 x ^{2}} d x

Apply Integral Substitution

= 7 \cdot \int \frac{1}{12 ( u ^{2} + 1 )} d u

Take the constant out:

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

= 7 \cdot \frac{1}{12} \cdot \int \frac{1}{u ^{2} + 1} d u

Use the common integral:

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

= 7 \cdot \frac{1}{12} arctan (u)

Substitute back

u = \frac{4}{3} x

= 7 \cdot \frac{1}{12} arctan (\frac{4}{3} x)

Simplify

7 \cdot \frac{1}{12} arctan (\frac{4}{3} x) : \frac{7}{12} arctan (\frac{4}{3} x)

= \frac{7}{12} arctan (\frac{4}{3} x)

Add a constant to the solution

= \frac{7}{12} arctan (\frac{4}{3} x) + C

(\frac{sin ( x )}{1 + cos ( x )})^{2}

\int x 3 x d x

f (x) = (x^{2} \cdot 3^{x})^{7}

\int (x^{n} n (x)) d x

t y^{^{'}} + 2 y = 4 t^{2}, y (1) = 2

What is the integral of 7/(9+16x^2) ?
The integral of 7/(9+16x^2) is 7/12 arctan(4/3 x)+C