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Using the double angle formula sinx=2sin(x2)cos(x2):2(2sin(x2)cos(x2)=2sin2(x2)Dividing both sides by 2 (assuming sin(x2)≠0):2cos(x2)=sin(x2) Step 6: Use the tangent functionThis can be rewritten as:tan(x2)=2 Step 7: Solve for xTaking the arctangent gives:x2=...
2、积分出来的结果不确定原因也有两个: 第一、由于有大量的代数、对数、三角的恒等式的出现, 可以在积分结果中互相替换;这种恒等式,在英文 中,用的的formulae。 第二、三角函数中有无数的恒等式,这个恒等式,在英文 中才是identity。3、举例如下:
右边大部分分子最好都比分母低一次幂：例如f(x)=(3x+5)/((x-1)(x^3-1))=(Ax+B)/((x-1...
#高等数学分析高数微积分calculus#瓦里斯wallis华里士点火formula积你太美！逆天海离薇求解反常定积分∫Ln(...
BOOK - RESONANCE ENGLISHCHAPTER - INDEFINITE INTEGRATION EXERCISE - Reduction Formulae 2videos INDEFINITE INTEGRATION BOOK - RESONANCE ENGLISHCHAPTER - INDEFINITE INTEGRATION EXERCISE - Exercise-2 Part-2 1videos INDEFINITE INTEGRATION BOOK - RESONANCE ENGLISHCHAPTER - INDEFINITE INTEGRATION EXERCISE - Sect...
sinx−siny=2cos(x+y2)sin(x−y2). So, we can rewrite the LHS as: sinx−sinycosx+cosy=2cos(x+y2)sin(x−y2)cosx+cosy. Step 2: Use the cosine sum formula We also know that cosx+cosy=2cos(x+y2)cos(x−y2). Now, we can substitute this into our expression: =2cos...
Using the formula for the integral of (1+t)−n: ∫(1+t)−ndt=(1+t)1−n1−n+C, for n=12: I=((1+t)1/21/2)10=2((1+t)1/2)10. Calculating the limits: =2((1+1)1/2−(1+0)1/2)=2(√2−1). Final resultThus, the value of the integral is: I=2(√2...
3.(the derivative of the denominator): - Differentiate: v=dx(2+cosx)=−sinx 4.Apply the quotient rule: - Substituteu,u′,v,andv′into the quotient rule formula: f′(x)=(3cosx+xsinx−2)(2+cosx)−(4sinx−2x−xcosx)(−sinx)(2+cosx)2 ...
Let: - u=x3secx- dv=(x2+6)(x3sinx+3x2cosx)2dx Then, we can compute the integral using integration by parts formula: ∫udv=uv−∫vdu. Step 8: Solve the IntegralAfter applying integration by parts and simplifying, we find: I=−x3secxx3sinx+3x2cosx+∫sec2xdx+C. Step 9: Final...