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Popular >

integral of (sin(x)-1)/(cos(x)+x)

Solution

\int \frac{sin ( x ) - 1}{cos ( x ) + x} d x

Solution

- ln ∣ cos (x) + x ∣ + C

Solution steps

\int \frac{sin ( x ) - 1}{cos ( x ) + x} d x

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - ln ∣ u ∣

Substitute back

u = cos (x) + x

= - ln ∣ cos (x) + x ∣

Add a constant to the solution

= - ln ∣ cos (x) + x ∣ + C

Popular Examples

integral of 0.5e^t

\int 0.5 e^{t} d t

integral of sqrt(x)+1/x

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

integral of (5x-(x^3)/2+(ARyx^2)/2+C)

\int (5 x - \frac{x ^{3}}{2} + \frac{A R y x ^{2}}{2} + C) d x

integral of 8/(x^3+4x)

\int \frac{8}{x ^{3} + 4 x} d x

integral of tan^5(x/3)

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

Frequently Asked Questions (FAQ)

What is the integral of (sin(x)-1)/(cos(x)+x) ?
The integral of (sin(x)-1)/(cos(x)+x) is -ln|cos(x)+x|+C