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Step-by-step Solution

Solve the trigonometric integral $\int\sec\left(1-4x\right)^3dx$

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Step-by-step explanation

Problem to solve:

$\int\sec^3\left(1-4x\right)dx$

Learn how to solve trigonometric integrals problems step by step online.

$\begin{matrix}u=1-4x \\ du=-4dx\end{matrix}$

Unlock this full step-by-step solution!

Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(sec(1-4*x)^3)dx. Solve the integral \int\sec\left(1-4x\right)^3dx applying u-substitution. Let u and du be. Isolate dx in the previous equation. Substituting u and dx in the integral and simplify. Take the constant out of the integral.

Answer

$-\frac{1}{8}\tan\left(1-4x\right)\sec\left(1-4x\right)-\frac{1}{8}\ln\left|\sec\left(1-4x\right)+\tan\left(1-4x\right)\right|+C_0$

Problem Analysis

$\int\sec^3\left(1-4x\right)dx$

Related formulas:

2. See formulas

Time to solve it:

~ 0.27 seconds