What is the integral of 3/(sqrt(1+x^2)) ?

The integral of 3/(sqrt(1+x^2)) is 3ln|sqrt(x^2+1)+x|+C

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integral of 3/(sqrt(1+x^2))

\int \frac{3}{1 + x ^{2}} d x

3 ln x^{2} + 1 + x + C

Solution steps

\int \frac{3}{1 + x ^{2}} d x

Take the constant out:

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

= 3 \cdot \int \frac{1}{1 + x ^{2}} d x

Use the common integral:

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

= 3 ln x^{2} + 1 + x

Add a constant to the solution

= 3 ln x^{2} + 1 + x + C

\frac{1}{( s - 1 ) ^{2} + 1}

f (x) = csc (x), at x = \frac{π}{6}

\frac{d}{d x} (y^{3} + x y^{2} + y)

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

\int_{- 1}^{1} (6 x^{5} + 3) d x

What is the integral of 3/(sqrt(1+x^2)) ?
The integral of 3/(sqrt(1+x^2)) is 3ln|sqrt(x^2+1)+x|+C