# Step-by-step Solution

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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.

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

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.

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

### Problem Analysis

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

### Main topic:

Trigonometric integrals

~ 0.27 seconds