Josh D.

asked • 03/23/24

Calculus Help!!!

Evaluate (an integral f) sec^2 (x)(1+tan^3(x))dx

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Doug C. answered • 03/23/24

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This is a u-sub.

Let u = tan x

du = sec2(x)dx


Integral becomes:

∫ (1+u3)du


Take it from there remembering to replace u with tanx and add a constant of integration.



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Josh D.

so will the answer be tanx +tan^4x/4 + C
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03/24/24

Doug C.

Yes, here is a verification. Use the technique here to check your work on other indefinite integrals, i.e. f(x) = integrand, F(x) = your answer, F'(x) should match the integrand. desmos.com/calculator/lni20loblx
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03/25/24

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