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Popular >

integral of 1/(6x+7)

Solution

\int \frac{1}{6 x + 7} d x

Solution

\frac{1}{6} ln ∣ 6 x + 7 ∣ + C

Solution steps

\int \frac{1}{6 x + 7} d x

Apply u-substitution

: \int \frac{1}{6 u} d u

= \int \frac{1}{6 u} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{6} ln ∣ u ∣

Substitute back

u = 6 x + 7

= \frac{1}{6} ln ∣ 6 x + 7 ∣

Add a constant to the solution

= \frac{1}{6} ln ∣ 6 x + 7 ∣ + C

Popular Examples

integral of 4\sqrt[3]{x^2}

integral of x^{10}+10^x

\int x^{10} + 1 0^{x} d x

integral of x^{1.2}+7x^{2.5}

\int x^{1.2} + 7 x^{2.5} d x

integral of arctan(x) 1/(1+x^2)

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

integral of (4x^2)/(sin(x^3-5))

\int \frac{4 x ^{2}}{sin ( x ^{3} - 5 )} d x

Frequently Asked Questions (FAQ)

What is the integral of 1/(6x+7) ?
The integral of 1/(6x+7) is 1/6 ln|6x+7|+C