What is the integral of 7arctan(3y) ?

The integral of 7arctan(3y) is 7(yarctan(3y)-1/6 ln|9y^2+1|)+C

Popular >

integral of 7arctan(3y)

\int 7 arctan (3 y) d y

7 (y arctan (3 y) - \frac{1}{6} ln 9 y^{2} + 1) + C

Solution steps

\int 7 arctan (3 y) d y

Take the constant out:

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

= 7 \cdot \int arctan (3 y) d y

Apply Integration By Parts

: y arctan (3 y) - \int \frac{3 y}{9 y ^{2} + 1} d y

= 7 (y arctan (3 y) - \int \frac{3 y}{9 y ^{2} + 1} d y)

\int \frac{3 y}{9 y ^{2} + 1} d y = \frac{1}{6} ln 9 y^{2} + 1

= 7 (y arctan (3 y) - \frac{1}{6} ln 9 y^{2} + 1)

Add a constant to the solution

= 7 (y arctan (3 y) - \frac{1}{6} ln 9 y^{2} + 1) + C

\int \frac{6 sin ( 2 x )}{sin ( x )} d x

n = 1 \sum \infty \frac{8}{π ^{n}}

\int sec^{2} (θ) + 7 d θ

y = \frac{5}{6} x^{2}, y = \frac{11}{6} - x^{2}

\frac{d}{d x} (e^{r x} r)

What is the integral of 7arctan(3y) ?
The integral of 7arctan(3y) is 7(yarctan(3y)-1/6 ln|9y^2+1|)+C