Using an appropriate substitution, $\int \tan^{10}(x)\sec^4(x)dx$ is equal to:
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Let's substitute u = sec(x). This means that du = sec(x)tan(x)dx. Now, let's rewrite the expression in terms of u: tan(x)(sec^2(x))dx = tan(x)(1 + tan^2(x))dx Using the substitution, we can rewrite this as: tan(x)(1 + tan^2(x))dx = (u - 1)du Now, we can Show more…
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