Final answer to the problem
$\frac{3}{16}x^{16}+\frac{60}{13}x^{13}+45x^{10}+\frac{1500}{7}x^{7}+\frac{1875}{4}x^{4}+60\sin\left(x\right)-60x\cos\left(x\right)-30x^{2}\sin\left(x\right)+C_0$
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Step-by-step Solution
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- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
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- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
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1
Multiplying the fraction by $\cos\left(x\right)$
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$\int3x^3\left(\left(x^3+5\right)^4+\frac{-10\cos\left(x\right)}{x}\right)dx$
Learn how to solve problems step by step online. Find the integral int(3x^3((x^3+5)^4+-10/xcos(x)))dx. Multiplying the fraction by \cos\left(x\right). Rewrite the integrand 3x^3\left(\left(x^3+5\right)^4+\frac{-10\cos\left(x\right)}{x}\right) in expanded form. Expand the integral \int\left(3x^{15}+60x^{12}+450x^{9}+1500x^{6}+1875x^3-30x^{2}\cos\left(x\right)\right)dx into 6 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int3x^{15}dx results in: \frac{3}{16}x^{16}.
Final answer to the problem
$\frac{3}{16}x^{16}+\frac{60}{13}x^{13}+45x^{10}+\frac{1500}{7}x^{7}+\frac{1875}{4}x^{4}+60\sin\left(x\right)-60x\cos\left(x\right)-30x^{2}\sin\left(x\right)+C_0$
