inverse of 4^{-x+1}-1

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

simplify solve for expand factor rationalize

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implicit derivative dydx , y=tan(xy)

Solution

dydx =ysec²(xy)1−xsec²(xy)

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Solution steps

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∫ sin(x−7)dx

Apply Integration By Parts: sin(x−7)x−∫ cos(x−7)xdx

=sin(x−7)x−∫ cos(x−7)xdx

∫ cos(x−7)xdx=−xsin(7−x)+cos(7−x)

=sin(x−7)x−(−xsin(7−x)+cos(7−x))

Simplify sin(x−7)x−(−xsin(7−x)+cos(7−x)): xsin(x−7)+xsin(7−x)−cos(7−x)

=xsin(x−7)+xsin(7−x)−cos(7−x)

Add a constant to the solution

=xsin(x−7)+xsin(7−x)−cos(7−x)+C

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