What is the integral of (4/(\sqrt[3]{x)}-tan(x)) ?

The integral of (4/(\sqrt[3]{x)}-tan(x)) is 6x^{2/3}+ln|cos(x)|+C

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integral of (4/(\sqrt[3]{x)}-tan(x))

6 x^{\frac{2}{3}} + ln ∣ cos (x) ∣ + C

Solution steps

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

\int tan (x) d x = - ln ∣ cos (x) ∣

= 6 x^{\frac{2}{3}} - (- ln ∣ cos (x) ∣)

Simplify

= 6 x^{\frac{2}{3}} + ln ∣ cos (x) ∣

Add a constant to the solution

= 6 x^{\frac{2}{3}} + ln ∣ cos (x) ∣ + C

\frac{d}{d x} (\frac{x}{x + 4})

\int \frac{1 + e ^{2 x}}{e ^{x - 1}} d x

\int 1 - \frac{3}{14 - x} d x

\int \frac{3}{x + 3 + x} d x

\frac{d y}{d t} + y = 7 t

What is the integral of (4/(\sqrt[3]{x)}-tan(x)) ?
The integral of (4/(\sqrt[3]{x)}-tan(x)) is 6x^{2/3}+ln|cos(x)|+C