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The integral of a function times a constant ($20$) is equal to the constant times the integral of the function
Learn how to solve trigonometric integrals problems step by step online.
$20\int\tan\left(x\right)^3dx$
Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(20tan(x)^3)dx. The integral of a function times a constant (20) is equal to the constant times the integral of the function. Use trig identites to rewrite the integral's argument \tan\left(x\right)^3 in an expanded form. Expand the integral \int\left(\tan\left(x\right)\sec\left(x\right)^2-\tan\left(x\right)\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\tan\left(x\right)\sec\left(x\right)^2dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that \sec\left(x\right) it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.