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We can solve the integral $\int5x\left(1-x^2\right)^3dx$ by applying integration method of trigonometric substitution using the substitution
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$x=\sin\left(\theta \right)$
Learn how to solve integral calculus problems step by step online. Find the integral int(5x(1-x^2)^3)dx. We can solve the integral \int5x\left(1-x^2\right)^3dx by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dx, we need to find the derivative of x. We need to calculate dx, we can do that by deriving the equation above. Substituting in the original integral, we get. We can solve the integral \int5\sin\left(\theta \right)\left(1-\sin\left(\theta \right)^2\right)^3\cos\left(\theta \right)d\theta 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 \sin\left(\theta \right) it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.