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Question Number 23752 Answers: 1 Comments: 0

∫_1 ^2 x^3 +1=?

$$\int_{\mathrm{1}} ^{\mathrm{2}} {x}^{\mathrm{3}} +\mathrm{1}=? \\ $$

Question Number 23679 Answers: 2 Comments: 0

Question Number 23677 Answers: 0 Comments: 0

solve lim_(x→inf+) ∫^(2(√x)) _(2sin(1/x)) ((2t^4 +1)/((t−3)(t^3 +3))) dt

$${solve} \\ $$$$\:\:\:\:\:\:\:\:\:\: \\ $$$$\underset{{x}\rightarrow{inf}+} {\mathrm{li}{m}}\:\:\underset{\mathrm{2}{sin}\frac{\mathrm{1}}{{x}}} {\int}^{\mathrm{2}\sqrt{{x}}} \frac{\mathrm{2}{t}^{\mathrm{4}} +\mathrm{1}}{\left({t}−\mathrm{3}\right)\left({t}^{\mathrm{3}} +\mathrm{3}\right)}\:{dt} \\ $$

Question Number 23663 Answers: 1 Comments: 3

solve ∫^1_ _(−1) x^2 d(lnx)

$${solve} \\ $$$$ \\ $$$$\underset{−\mathrm{1}} {\int}^{\mathrm{1}_{} } {x}^{\mathrm{2}} {d}\left({lnx}\right) \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 23592 Answers: 1 Comments: 0

Let ABC be a triangle with AB = AC and ∠BAC = 30°. Let A′ be the reflection of A in the line BC; B′ be the reflection of B in the line CA; C′ be the reflection of C in the line AB. Show that A′, B′, C′ form the vertices of an equilateral triangle.

$$\mathrm{Let}\:{ABC}\:\mathrm{be}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{with}\:{AB}\:=\:{AC} \\ $$$$\mathrm{and}\:\angle{BAC}\:=\:\mathrm{30}°.\:\mathrm{Let}\:{A}'\:\mathrm{be}\:\mathrm{the}\:\mathrm{reflection} \\ $$$$\mathrm{of}\:{A}\:\mathrm{in}\:\mathrm{the}\:\mathrm{line}\:{BC};\:{B}'\:\mathrm{be}\:\mathrm{the}\:\mathrm{reflection} \\ $$$$\mathrm{of}\:{B}\:\mathrm{in}\:\mathrm{the}\:\mathrm{line}\:{CA};\:{C}'\:\mathrm{be}\:\mathrm{the}\:\mathrm{reflection} \\ $$$$\mathrm{of}\:{C}\:\mathrm{in}\:\mathrm{the}\:\mathrm{line}\:{AB}.\:\mathrm{Show}\:\mathrm{that}\:{A}',\:{B}',\:{C}' \\ $$$$\mathrm{form}\:\mathrm{the}\:\mathrm{vertices}\:\mathrm{of}\:\mathrm{an}\:\mathrm{equilateral} \\ $$$$\mathrm{triangle}. \\ $$

Question Number 23539 Answers: 1 Comments: 0

∫tan^6 x dx

$$\int\mathrm{tan}\:^{\mathrm{6}} \mathrm{x}\:\mathrm{dx} \\ $$

Question Number 23477 Answers: 0 Comments: 0

Find the value of x, ∫_(−∞) ^x dx = ∫∣± sinh cot ln (15−(√(33+x)))∣ dx

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}, \\ $$$$\:\:\:\:\:\:\:\int_{−\infty} ^{{x}} {d}\mathrm{x}\:=\:\int\mid\pm\:\mathrm{sinh}\:\mathrm{cot}\:\mathrm{ln}\:\left(\mathrm{15}−\sqrt{\mathrm{33}+{x}}\right)\mid\:\mathrm{dx} \\ $$

Question Number 23418 Answers: 1 Comments: 0

∫sec^2 (√x) /(√x) dx

$$\int\mathrm{sec}\:^{\mathrm{2}} \sqrt{\mathrm{x}}\:/\sqrt{\mathrm{x}}\:\mathrm{dx} \\ $$

Question Number 23408 Answers: 1 Comments: 0