What is the integral of 4/(x^2-14x+50) ?

The integral of 4/(x^2-14x+50) is 4arctan(x-7)+C

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integral of 4/(x^2-14x+50)

\int \frac{4}{x ^{2} - 14 x + 50} d x

4 arctan (x - 7) + C

Solution steps

\int \frac{4}{x ^{2} - 14 x + 50} d x

Take the constant out:

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

= 4 \cdot \int \frac{1}{x ^{2} - 14 x + 50} d x

Complete the square

x^{2} - 14 x + 50 : (x - 7)^{2} + 1

= 4 \cdot \int \frac{1}{( x - 7 ) ^{2} + 1} d x

Apply u-substitution

: \int \frac{1}{u ^{2} + 1} d u

= 4 \cdot \int \frac{1}{u ^{2} + 1} d u

Use the common integral:

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

= 4 arctan (u)

Substitute back

u = x - 7

= 4 arctan (x - 7)

Add a constant to the solution

= 4 arctan (x - 7) + C

\int_{0}^{4} (3 t - 2 e^{t}) d t

\frac{d}{d x} (x^{2} - 16)

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\int_{- 2}^{5} (x^{2} - 4) d x

\frac{d}{d x} ((5 x^{4} - 6 x^{3} + x)^{5})

What is the integral of 4/(x^2-14x+50) ?
The integral of 4/(x^2-14x+50) is 4arctan(x-7)+C