$\int \frac{4 x^{3}+\cos x}{x^{4}+\sin x} d x=\ln \left|x^{4}+\sin x\right|+C$ .

Name: $\int \frac{4 x^{3}+\cos x}{x^{4}+\sin x} d x=\ln \left|x^{4}+\sin x\right|+C$ .
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Question

Quizplus · Accepted Answer

The integral $\int \frac{4 x^{3}+\cos x}{x^{4}+\sin x} d x$ simplifies to $\ln \left|x^{4}+\sin x\right|+C$ because the derivative of the denominator $x^{4}+\sin x$ is exactly the numerator $4x^{3}+\cos x$, making it a direct application of the integral of the form $\int \frac{f'(x)}{f(x)} dx = \ln|f(x)| + C$.

∫4x3+cos⁡xx4+sin⁡xdx=ln⁡∣x4+sin⁡x∣+C\int \frac{4 x^{3}+\cos x}{x^{4}+\sin x} d x=\ln \left|x^{4}+\sin x\right|+C∫x4+sinx4x3+cosx​dx=ln​x4+sinx​+C

$\int \frac{4 x^{3}+\cos x}{x^{4}+\sin x} d x=\ln \left|x^{4}+\sin x\right|+C$