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Popular >

integral of 7/(xsqrt(x^2-1))

Solution

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

Solution

7 arctan (x^{2} - 1) + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

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

= 7 arctan (u)

Substitute back

u = x^{2} - 1

= 7 arctan (x^{2} - 1)

Add a constant to the solution

= 7 arctan (x^{2} - 1) + C

Popular Examples

integral of (5x+6)/(x^2+3x+2)

\int \frac{5 x + 6}{x ^{2} + 3 x + 2} d x

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\int x^{6} sin (x^{7} + 8) d x

integral of 1/(sqrt(x)(1-\sqrt{x))^3}

\int \frac{1}{x ( 1 - x ) ^{3}} d x

integral of 4/(5+6x)

\int \frac{4}{5 + 6 x} d x

integral of 3/((5x-2)^2)

\int \frac{3}{( 5 x - 2 ) ^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral of 7/(xsqrt(x^2-1)) ?
The integral of 7/(xsqrt(x^2-1)) is 7arctan(sqrt(x^2-1))+C