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Calculate antiderivatives of a subtraction

Fill in the blank.
If f(x)=8/x and g(x)=1/x², then $\int_{ }^{ }\left[f\left(x\right)-g\left(x\right)\right]dx=$

$8\ln x+\frac{1}{x}+c$

$\ln x-\frac{1}{x}+c$

$7\ln x+\frac{1}{x}+c$

Fill in the blank.
If f(x)=15x¹⁴ and g(x)=x¹⁵, then $\int_{ }^{ }\left[f\left(x\right)-g\left(x\right)\right]dx$

$x^{15}-\frac{x^{16}}{16}+c$

$x^5-\frac{x^6}{6}$

$x^{15}-\frac{x^{16}}{16}+c$

Complete this statement:
If f (x)=4x and g(x)=x³ then ∫[f(x) - g(x)] dx = ___________.

$2x^2-\frac{x^3}{3}+c$

$2x^2-\frac{x^4}{4}+c$

$4x+\frac{x^3}{3}+c$

Complete this statement:
If f (x)=Cos x and g(x)=x² then ∫[f(x) - g(x)] dx = ___________.

$\sin x+\frac{x^3}{3}+c$

$4x+\frac{x^3}{3}+c$

$\sin x-\frac{x^3}{3}+c$

Fill in the blank.
If f(x)=x¹²⁴ and g(x)=x¹¹⁵, then $\int_{ }^{ }\left[f\left(x\right)-g\left(x\right)\right]dx=$

$\frac{x^{125}}{125}-\frac{x^{116}}{116}+c$

$\frac{x^{125}}{125}+\frac{x^{116}}{116}$

$\frac{x^{125}}{125}-\frac{x^{116}}{116}$

Fill in the blank.
If f(x)=sinsin7x and g(x)=e^9x,then $\int_{ }^{ }\left[f\left(x\right)-g\left(x\right)\right]dx=$

$-\frac{\cos\cos7x}{7}-\frac{e^{9x}}{9}+c$

$-\frac{\cos\cos4x}{4}+\frac{e^{7x}}{7}+c$

$-\frac{\cos\cos4x}{4}+\frac{e^{7x}}{7}$

Fill in the blank.
If f(x)=3x and g(x)=x⁷, then $\int_{ }^{ }\left[f\left(x\right)-g\left(x\right)\right]dx=$

$-\frac{\cot\cot3x}{3}-\frac{x^8}{8}+c$

$\frac{\cot\cot3x}{3}+\frac{x^8}{8}+c$

$\frac{\cot\cot3x}{3}+\frac{x^8}{8}$

Fill in the blank.
If f(x)=5x⁴ and g(x)=12e^12x, then $\int_{ }^{ }\left[f\left(x\right)-g\left(x\right)\right]dx=$

$x^5-e^{12x}+c$

$x^5+e^{12x}+c$

$x^5-e^{2x}$

Complete this statement:
If f (x)=4x and g(x)=x² then ∫[f(x) - g(x)] dx = ___________.

$2x^2-4x+c$

$2x^2-\frac{x^3}{3}+c$

$\frac{x^3}{3}+c$

Fill in the blank.
If f(x)=5/x and g(x)=5e^5x, then $\int_{ }^{ }\left[f\left(x\right)-g\left(x\right)\right]dx$

$5\ln x+e^{5x}+c$

$e^{5x}+c$

$5\ln x-e^{5x}+c$

Questions

Time

Score

Calculate antiderivatives of a subtraction

Fill in the blank.If f(x)=8/x and g(x)=1/x2, then ﻿∫[f(x)−g(x)]dx=\int_{ }^{ }\left[f\left(x\right)-g\left(x\right)\right]dx=∫​[f(x)−g(x)]dx=﻿

﻿8ln⁡x+1x+c8\ln x+\frac{1}{x}+c8lnx+x1​+c﻿

﻿ln⁡x−1x+c\ln x-\frac{1}{x}+clnx−x1​+c﻿

﻿7ln⁡x+1x+c7\ln x+\frac{1}{x}+c7lnx+x1​+c﻿

Fill in the blank.If f(x)=15x14 and g(x)=x15, then ﻿∫[f(x)−g(x)]dx\int_{ }^{ }\left[f\left(x\right)-g\left(x\right)\right]dx∫​[f(x)−g(x)]dx﻿

﻿x15−x1616+cx^{15}-\frac{x^{16}}{16}+cx15−16x16​+c﻿

﻿x5−x66x^5-\frac{x^6}{6}x5−6x6​﻿

﻿x15−x1616+cx^{15}-\frac{x^{16}}{16}+cx15−16x16​+c﻿

Complete this statement: If f (x)=4x and g(x)=x3 then ∫[f(x) - g(x)] dx = ___________.

﻿2x2−x33+c2x^2-\frac{x^3}{3}+c2x2−3x3​+c﻿

﻿2x2−x44+c2x^2-\frac{x^4}{4}+c2x2−4x4​+c﻿

﻿4x+x33+c4x+\frac{x^3}{3}+c4x+3x3​+c﻿

Complete this statement: If f (x)=Cos x and g(x)=x2 then ∫[f(x) - g(x)] dx = ___________.

﻿sin⁡x+x33+c\sin x+\frac{x^3}{3}+csinx+3x3​+c﻿

﻿4x+x33+c4x+\frac{x^3}{3}+c4x+3x3​+c﻿

﻿sin⁡x−x33+c\sin x-\frac{x^3}{3}+csinx−3x3​+c﻿

Fill in the blank.If f(x)=x124 and g(x)=x115, then ﻿∫[f(x)−g(x)]dx=\int_{ }^{ }\left[f\left(x\right)-g\left(x\right)\right]dx=∫​[f(x)−g(x)]dx=﻿

﻿x125125−x116116+c\frac{x^{125}}{125}-\frac{x^{116}}{116}+c125x125​−116x116​+c﻿

﻿x125125+x116116\frac{x^{125}}{125}+\frac{x^{116}}{116}125x125​+116x116​﻿

﻿x125125−x116116\frac{x^{125}}{125}-\frac{x^{116}}{116}125x125​−116x116​﻿

Fill in the blank.If f(x)=sinsin7x and g(x)=e9x,then ﻿∫[f(x)−g(x)]dx=\int_{ }^{ }\left[f\left(x\right)-g\left(x\right)\right]dx=∫​[f(x)−g(x)]dx=﻿

﻿−cos⁡cos⁡7x7−e9x9+c-\frac{\cos\cos7x}{7}-\frac{e^{9x}}{9}+c−7coscos7x​−9e9x​+c﻿

﻿−cos⁡cos⁡4x4+e7x7+c-\frac{\cos\cos4x}{4}+\frac{e^{7x}}{7}+c−4coscos4x​+7e7x​+c﻿

﻿−cos⁡cos⁡4x4+e7x7-\frac{\cos\cos4x}{4}+\frac{e^{7x}}{7}−4coscos4x​+7e7x​﻿

Fill in the blank.If f(x)=3x and g(x)=x7, then ﻿∫[f(x)−g(x)]dx=\int_{ }^{ }\left[f\left(x\right)-g\left(x\right)\right]dx=∫​[f(x)−g(x)]dx=﻿

﻿−cot⁡cot⁡3x3−x88+c-\frac{\cot\cot3x}{3}-\frac{x^8}{8}+c−3cotcot3x​−8x8​+c﻿

﻿cot⁡cot⁡3x3+x88+c\frac{\cot\cot3x}{3}+\frac{x^8}{8}+c3cotcot3x​+8x8​+c﻿

﻿cot⁡cot⁡3x3+x88\frac{\cot\cot3x}{3}+\frac{x^8}{8}3cotcot3x​+8x8​﻿

Fill in the blank.If f(x)=5x4 and g(x)=12e12x, then ﻿∫[f(x)−g(x)]dx=\int_{ }^{ }\left[f\left(x\right)-g\left(x\right)\right]dx=∫​[f(x)−g(x)]dx=﻿

﻿x5−e12x+cx^5-e^{12x}+cx5−e12x+c﻿

﻿x5+e12x+cx^5+e^{12x}+cx5+e12x+c﻿

﻿x5−e2xx^5-e^{2x}x5−e2x﻿

Complete this statement: If f (x)=4x and g(x)=x2 then ∫[f(x) - g(x)] dx = ___________.

﻿2x2−4x+c2x^2-4x+c2x2−4x+c﻿

﻿2x2−x33+c2x^2-\frac{x^3}{3}+c2x2−3x3​+c﻿

﻿x33+c\frac{x^3}{3}+c3x3​+c﻿

Fill in the blank.If f(x)=5/x and g(x)=5e5x, then ﻿∫[f(x)−g(x)]dx\int_{ }^{ }\left[f\left(x\right)-g\left(x\right)\right]dx∫​[f(x)−g(x)]dx﻿

﻿5ln⁡x+e5x+c5\ln x+e^{5x}+c5lnx+e5x+c﻿

﻿e5x+ce^{5x}+ce5x+c﻿

﻿5ln⁡x−e5x+c5\ln x-e^{5x}+c5lnx−e5x+c﻿

Incorrect

Great!

Fill in the blank.
If f(x)=8/x and g(x)=1/x², then $\int_{ }^{ }\left[f\left(x\right)-g\left(x\right)\right]dx=$

$8\ln x+\frac{1}{x}+c$

$\ln x-\frac{1}{x}+c$

$7\ln x+\frac{1}{x}+c$

Fill in the blank.
If f(x)=15x¹⁴ and g(x)=x¹⁵, then $\int_{ }^{ }\left[f\left(x\right)-g\left(x\right)\right]dx$

$x^{15}-\frac{x^{16}}{16}+c$

$x^5-\frac{x^6}{6}$

$x^{15}-\frac{x^{16}}{16}+c$

Complete this statement:
If f (x)=4x and g(x)=x³ then ∫[f(x) - g(x)] dx = ___________.

$2x^2-\frac{x^3}{3}+c$

$2x^2-\frac{x^4}{4}+c$

$4x+\frac{x^3}{3}+c$

Complete this statement:
If f (x)=Cos x and g(x)=x² then ∫[f(x) - g(x)] dx = ___________.

$\sin x+\frac{x^3}{3}+c$

$4x+\frac{x^3}{3}+c$

$\sin x-\frac{x^3}{3}+c$

Fill in the blank.
If f(x)=x¹²⁴ and g(x)=x¹¹⁵, then $\int_{ }^{ }\left[f\left(x\right)-g\left(x\right)\right]dx=$

$\frac{x^{125}}{125}-\frac{x^{116}}{116}+c$

$\frac{x^{125}}{125}+\frac{x^{116}}{116}$

$\frac{x^{125}}{125}-\frac{x^{116}}{116}$

Fill in the blank.
If f(x)=sinsin7x and g(x)=e^9x,then $\int_{ }^{ }\left[f\left(x\right)-g\left(x\right)\right]dx=$

$-\frac{\cos\cos7x}{7}-\frac{e^{9x}}{9}+c$

$-\frac{\cos\cos4x}{4}+\frac{e^{7x}}{7}+c$

$-\frac{\cos\cos4x}{4}+\frac{e^{7x}}{7}$

Fill in the blank.
If f(x)=3x and g(x)=x⁷, then $\int_{ }^{ }\left[f\left(x\right)-g\left(x\right)\right]dx=$

$-\frac{\cot\cot3x}{3}-\frac{x^8}{8}+c$

$\frac{\cot\cot3x}{3}+\frac{x^8}{8}+c$

$\frac{\cot\cot3x}{3}+\frac{x^8}{8}$

Fill in the blank.
If f(x)=5x⁴ and g(x)=12e^12x, then $\int_{ }^{ }\left[f\left(x\right)-g\left(x\right)\right]dx=$

$x^5-e^{12x}+c$

$x^5+e^{12x}+c$

$x^5-e^{2x}$

Complete this statement:
If f (x)=4x and g(x)=x² then ∫[f(x) - g(x)] dx = ___________.

$2x^2-4x+c$

$2x^2-\frac{x^3}{3}+c$

$\frac{x^3}{3}+c$

Fill in the blank.
If f(x)=5/x and g(x)=5e^5x, then $\int_{ }^{ }\left[f\left(x\right)-g\left(x\right)\right]dx$

$5\ln x+e^{5x}+c$

$e^{5x}+c$

$5\ln x-e^{5x}+c$