How is calculus calculated?

Methods of indefinite integral substitution substitution method substitution method (1): Let f (U) have the original function f (U), u = g (x) differentiable, then f [g (x)] is the original function of F [g (x)] g '(x)

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1. Integral: (1), ∫ (π / 2,0) sin θ cos ^ 3 (θ) d θ; (2), ∫ (π, 0) [1-sin ^ 3 (θ)] d θ; (3), ∫ (4,1) DX / (1 + √ x) thank you! And: (4), ∫ (π, 0) √ [1 + cos (2x)] DX; (5)、∫(1,0)xe^(-x)dx; (6)、∫(e,1)xln(x)dx; I'm not a student, I just want results,
2. The problem of three integrals 1. ∫ 16sin ^ 4 (x) DX 2. ∫ 1 / (XLN (x)) DX 3. ∫ sin ^ 3 (x) cos (x) DX 1.∫16sin^4(x) dx 2.∫1/(xln(x)) dx 3.∫sin^3(x)cos(x) dx
3. What is ∫ (COS & sup3; X / Sin & sup2; x) DX
4. Cos (x / 2) cos (NX) DX (0 → π) definite integral
5. How does √ (1 + sin α) turn into √ "(sin (α / 2) + cos (α / 2)) &# 178;" and | sin (α / 2) + cos (α / 2) | and which formula is used
6. The answer is that (Sin & # 178; a + cos & # 178; a) / (Sin & # 178; a + cos & # 178; a-sinacosa) protolith can be transformed into this
7. If the function f (x) = x & # 178; - (A-1) x + 5 is an increasing function in the interval (1 / 2,1), the value range of F (2) can be obtained
8. Given that the function f (x) = 4x & # 178; - MX + 5 is an increasing function in the interval [- 2, + ∞), then the range of F (- 1) is_____ .
9. The known function f (x) = f '(1) e ^ x-1-f (0) x + &# 189; X & # 178; If f (x) ≥ (1 / 2) x & # 178; + ax + B, find the maximum of (a + 1) B
10. The known function f (x) = - X & # 178; - 2| x | + 3 (1) Write f (x) in the form of piecewise function. (2) write the monotone increasing and decreasing interval of the function. (3) write the range of the function (3) It is pointed out that
11. How to calculate ∫ cos (x / 2) ^ 2DX?
12. The calculation of calculus How to solve indefinite integral for compound function For example, how can X / (1 + x), sin2x find their indefinite integrals
13. What about calculus Xdx (X-5) for 5 to 10 interval integral how to calculate? To each step of the calculation steps!
14. How to calculate the approximate value of cos29
15. Use calculus to get the approximate value of ln1.03!
16. Calculus approximation problem e - 0.1 power approximation. To the process, thank you
17. Approximate value of cos29
18. How much is cos29? Decomposition by micro product, I hope there is a process There are three times how to solve the root 996. I didn't listen to it when I talked about it
19. The lower limit is - 90 ° and the upper limit is the integral of 90 ° arctan (e ^ x) + arctan (e ^ - x) DX
20. ∫(0→1) arctan(e^x)/e^x dx