Dsinx-sin3x [3] sin³x = find D and E. %D E

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A: Given ∫ (a2- x2)32 dx Perform trignometric substitution x= aSin (μ) →υ= arcsin (xa), dx= acos (μ)…

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A: The given integral is: I=∫x4x5+33dx    ...1 As we know the Power Rule: ∫xndx=xn+1n+1+C

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A: we…

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A: As we know that the Power rule: ∫xndx=xn+1n+1,n≠-1 1). From the given problem I=∫561x2dx So,…

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A: We will solve the integration by the substitution, t = ex

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A: To evaluate: ∫extan3(ex)sec (ex)3dx

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A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Find x?e**dx Sx²

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A: First we put sin-1(x/9)=t and differentiate both side with respect to t and then solve it. Follow…

Q: 2x dx et

A: We have  given  to find integral  I=∫e2x+1eXdx I=∫e2xexdx +∫1exdx I=∫exdx+∫e-xdx I=ex+-e-x+C…

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A: Evaluate: ∫abc2x-3 dx

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A: To solve the given definite integral problem.

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A: Given integral is: ∫11-cosxdx

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A: ∫coth3xsinh3xdx=-cosech3x3+C           where C is an integral constant.

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A: Given: The integral is  ∫xtan-1x dx     Formula used: Integration by parts: ∫udv=uv-∫vdu

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A: From the given problem: I=∫x-ax2+k2dx So, we can also write as:…

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A: Given,        ∫0∞x6e-3xdx